{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulation for Finance Modeling\n",
    "Franklin Ma    <a href='mailto:franklin.ma@berkeley.edu'>franklin.ma@berkeley.edu</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Contact**       \n",
    " \n",
    "**Data Application Lab** | <a href='http://datalaus.com' target='_blank'>www.datalaus.com</a>\n",
    "\n",
    "**Contact us** | <a href='mailto:info@datalaus.com'>info@datalaus.com</a>   \n",
    "\n",
    "**Office phone** | 1-(800)-485-7918"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "uuid": "fba5b184-6652-4665-9053-1741d9b16bb9"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.random as npr\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "uuid": "8763b99e-6b02-4003-8567-c0f505986e5a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.25199969,  0.48591204,  0.57089262,  0.37486029,  0.6296201 ,\n",
       "        0.69265906,  0.28958098,  0.9637495 ,  0.71704386,  0.65857454])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "uuid": "16f2a7c4-62dd-4d0f-bde9-fafb61e0fb64"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.19851692,  0.52519068,  0.84843508,  0.32962508,  0.27780781],\n",
       "       [ 0.03894175,  0.64062059,  0.9223895 ,  0.838284  ,  0.1436538 ],\n",
       "       [ 0.59469956,  0.95524137,  0.82462688,  0.47689168,  0.00369095],\n",
       "       [ 0.44169501,  0.51938312,  0.36187768,  0.9345898 ,  0.6190133 ],\n",
       "       [ 0.42771246,  0.97761364,  0.59939704,  0.7293766 ,  0.32744271]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(5, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "uuid": "2d14b433-a7da-4aac-a534-56ab4c8a5d84"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.53728343,  9.64871395,  6.27737777,  9.07893882,  8.90151259,\n",
       "        7.01412422,  5.65312627,  8.38644694,  6.99588963,  9.1798317 ])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 5.\n",
    "b = 10.\n",
    "npr.rand(10) * (b - a) + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "uuid": "a05adb2b-5704-4189-b0e8-19318ac3f0b9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.23816865,  9.02341247,  6.36738309,  6.39760504,  5.26745336],\n",
       "       [ 8.14161037,  6.26899043,  6.61681932,  9.91810756,  6.47948833],\n",
       "       [ 5.08757721,  8.89302802,  6.90262782,  7.95707514,  5.91281367],\n",
       "       [ 9.59605494,  9.80101062,  5.01276756,  5.5826808 ,  9.65509537],\n",
       "       [ 5.98375595,  7.34192285,  7.60397374,  7.97986246,  9.09488539]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(5, 5) * (b - a) + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "uuid": "4618b170-6bd3-4500-905a-0fe402f198c1"
   },
   "outputs": [],
   "source": [
    "sample_size = 500\n",
    "rn1 = npr.rand(sample_size, 3)\n",
    "rn2 = npr.randint(0, 10, sample_size)\n",
    "rn3 = npr.sample(size=sample_size)\n",
    "a = [0, 25, 50, 75, 100]\n",
    "rn4 = npr.choice(a, size=sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "uuid": "d03c9514-c224-4d2b-ad2a-9285058823b0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iT/8+BusZ/j7yttex0d9++ufr7E+TBzILa2B2N1Fmvhp4TdfZB1m8eC82b34w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\nrDyUxaAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3d5c630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2,\n",
    "                                             figsize=(7, 7))\n",
    "ax1.hist(rn1, bins=25, stacked=True)\n",
    "ax1.set_title('rand')\n",
    "ax1.set_ylabel('frequency')\n",
    "ax1.grid(True)\n",
    "ax2.hist(rn2, bins=25)\n",
    "ax2.set_title('randint')\n",
    "ax2.grid(True)\n",
    "ax3.hist(rn3, bins=25)\n",
    "ax3.set_title('sample')\n",
    "ax3.set_ylabel('frequency')\n",
    "ax3.grid(True)\n",
    "ax4.hist(rn4, bins=25)\n",
    "ax4.set_title('choice')\n",
    "ax4.grid(True)\n",
    "# tag: rand_samples\n",
    "# title: Simple pseudo-random numbers\n",
    "# size: 70"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "uuid": "fb2966ea-91ff-49c7-80e6-24bd6162cc5a"
   },
   "outputs": [],
   "source": [
    "sample_size = 500\n",
    "rn1 = npr.standard_normal(sample_size)\n",
    "rn2 = npr.normal(100, 20, sample_size)\n",
    "rn3 = npr.chisquare(df=0.5, size=sample_size)\n",
    "rn4 = npr.poisson(lam=1.0, size=sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "uuid": "3f790711-f965-4a10-b3df-47cc85d708d3"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VSmA0M12/jMxyr7/V2iU5v5PN16bHxsboIX0VU63mX/Oa49iwYXzCfs6bN58L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\nEEIlOsSWepueTtxobKQ6Mtrzq9HYWPTaVcm5ecc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      "text/plain": [
       "<matplotlib.figure.Figure at 0x8f89be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2, figsize=(7, 7))\n",
    "ax1.hist(rn1, bins=25)\n",
    "ax1.set_title('standard normal')\n",
    "ax1.set_ylabel('frequency')\n",
    "ax1.grid(True)\n",
    "ax2.hist(rn2, bins=25)\n",
    "ax2.set_title('normal(100, 20)')\n",
    "ax2.grid(True)\n",
    "ax3.hist(rn3, bins=25)\n",
    "ax3.set_title('chi square')\n",
    "ax3.set_ylabel('frequency')\n",
    "ax3.grid(True)\n",
    "ax4.hist(rn4, bins=25)\n",
    "ax4.set_title('Poisson')\n",
    "ax4.grid(True)\n",
    "# tag: rand_distris\n",
    "# title: Pseudo-random numbers from different distributions\n",
    "# size: 70"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Variables Generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "uuid": "ac34499c-4675-457e-a0ac-40b8efcdb72e"
   },
   "outputs": [],
   "source": [
    "S0 = 100  # initial value\n",
    "r = 0.05  # constant short rate\n",
    "sigma = 0.25  # constant volatility\n",
    "T = 2.0  # in years\n",
    "I = 10000  # number of random\n",
    "ST1 = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "             + sigma * np.sqrt(T) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "uuid": "7fc0b66a-9ce3-4c5e-bb99-d5e0363a6678"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NAJLWAOuA04A3Ap9U+ef9UMhzjrRIHaBNnuOUZy5nqseZmjNnMZF0KHBtRFwZEf8qIt5a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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9047b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ST1, bins=50)\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: gbm_T_sn\n",
    "# title: Simulated geometric Brownian motion (via +standard_normal+)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "uuid": "c37a0783-81b1-449f-924e-f792ba5017aa"
   },
   "outputs": [],
   "source": [
    "ST2 = S0 * npr.lognormal((r - 0.5 * sigma ** 2) * T,\n",
    "                        sigma * np.sqrt(T), size=I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "uuid": "fea07d0c-7fc1-4ab8-8b21-fc36e73c3151"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YtJ7rgLfBC+fmmoiI+5ZY3qwRHkzM9nd3RPwgsvMM7SC70twpwK6I2JUv87me\n5c8GNubX1OgAhwEvz3/+QuBaoBMRdy6z3b7rAW4A3povs4HsTMJLLW/WiEOaDmCWmGd67j/Pvr+R\nQdemEPAbEbGzz3OvAp4GXlZguwPXI+nHkl5DdoTyOz1PLVp+wZlgzWrjIxOzpS9iBPAdYG1+Om6A\nd/Q8dzPZtFi2Imkq//dosqmuXwFeKuk3ltlG3/Xkvgj8AfBTEfGtAsub1c6DidngTz8FQEQ8Q3ZE\ncGNegO/2LPNR4FBJD0j6FvBv8/Y/Bj4VEY8Cvw18TNJPL5Ghdz0P9qwH4MtkRyVf7Gn7d0ssb1Y7\nn4LezMxK85GJmZmV5sHEzMxK82BiZmaleTAxM7PSPJiYmVlpHkzMzKw0DyZmZlaaBxMzMyvt/wOO\nS9wZZ+XpRwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7768048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ST2, bins=50)\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: gbm_T_ln\n",
    "# title: Simulated geometric Brownian motion (via +lognormal+)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "uuid": "e5e17dcf-21f4-42ee-bcec-21103aaa8bb3"
   },
   "outputs": [],
   "source": [
    "import scipy.stats as scs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "uuid": "d6f800c9-f38f-4fe1-8cb5-fe9253f1194c"
   },
   "outputs": [],
   "source": [
    "def print_statistics(a1, a2):\n",
    "    ''' Prints selected statistics.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    a1, a2 : ndarray objects\n",
    "        results object from simulation\n",
    "    '''\n",
    "    sta1 = scs.describe(a1)\n",
    "    sta2 = scs.describe(a2)\n",
    "    print \"%14s %14s %14s\" % \\\n",
    "        ('statistic', 'data set 1', 'data set 2')\n",
    "    print 45 * \"-\"\n",
    "    print \"%14s %14.3f %14.3f\" % ('size', sta1[0], sta2[0])\n",
    "    print \"%14s %14.3f %14.3f\" % ('min', sta1[1][0], sta2[1][0])\n",
    "    print \"%14s %14.3f %14.3f\" % ('max', sta1[1][1], sta2[1][1])\n",
    "    print \"%14s %14.3f %14.3f\" % ('mean', sta1[2], sta2[2])\n",
    "    print \"%14s %14.3f %14.3f\" % ('std', np.sqrt(sta1[3]), np.sqrt(sta2[3]))\n",
    "    print \"%14s %14.3f %14.3f\" % ('skew', sta1[4], sta2[4])\n",
    "    print \"%14s %14.3f %14.3f\" % ('kurtosis', sta1[5], sta2[5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "uuid": "980679e8-56af-49e3-85f3-4b4d1ed90312"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         24.610         19.242\n",
      "           max        413.988        419.149\n",
      "          mean        110.928        110.032\n",
      "           std         40.920         39.963\n",
      "          skew          1.203          1.077\n",
      "      kurtosis          2.773          2.246\n"
     ]
    }
   ],
   "source": [
    "print_statistics(ST1, ST2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stochastic Processes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Geometric Brownian Motion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "uuid": "a6b64214-0041-49cb-b7a8-7b4965d1d03a"
   },
   "outputs": [],
   "source": [
    "I = 10000\n",
    "M = 50\n",
    "dt = T / M\n",
    "S = np.zeros((M + 1, I))\n",
    "S[0] = S0\n",
    "for t in range(1, M + 1):\n",
    "    S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "            + sigma * np.sqrt(dt) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "uuid": "969180df-b1f3-4f6d-8ec6-21cadbec06f1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6VwNPdq13oBizRc2kDqAxZmZmUofQGM5FybmoTz/nmTxBfnfFncBfzw1GxO8ud6OS3gp0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\nxcTMzCpzMTEzs8pcTMzMrLL/D63nhtWg04dVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa4d5c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(S[-1], bins=50)\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: gbm_dt_hist\n",
    "# title: Simulated geometric Brownian motion at maturity\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "uuid": "37d83fc1-6b2d-4d94-a5d1-75d2ba569283"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         23.632         19.242\n",
      "           max        459.354        419.149\n",
      "          mean        110.133        110.032\n",
      "           std         40.166         39.963\n",
      "          skew          1.134          1.077\n",
      "      kurtosis          2.648          2.246\n"
     ]
    }
   ],
   "source": [
    "print_statistics(S[-1], ST2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "scrolled": true,
    "uuid": "c424f261-aa3f-4b04-9b5d-bb6824107fa0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Zq1aWlkpiQsy1mK6toihuiqIEAPgZgDcA6c9WSigvPuD+/iJqw6hRxtdRXvrC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txnLFSVRfsXMW71OObtnkdkaCSDWg7il61+ybqkdUzbNo1VX1eHGdOpWHcPIyYu5p4WP+M3/Rqx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\nfLIkYYwxxqf/B28f1QWSfIbpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x96d3dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(S[:,0:10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: gbm_dt_paths\n",
    "# title: Simulated geometric Brownian motion paths\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### CIR Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "uuid": "b00481e7-074a-4d04-a65d-4ee95f971116"
   },
   "outputs": [],
   "source": [
    "x0 = 0.05\n",
    "kappa = 3.0\n",
    "theta = 0.02\n",
    "sigma = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "uuid": "e085f53a-d065-424e-b1f4-d41c64464c2a"
   },
   "outputs": [],
   "source": [
    "I = 10000\n",
    "M = 50\n",
    "dt = T / M\n",
    "def srd_euler():\n",
    "    xh = np.zeros((M + 1, I))\n",
    "    x1 = np.zeros_like(xh)\n",
    "    xh[0] = x0\n",
    "    x1[0] = x0\n",
    "    for t in range(1, M + 1):\n",
    "        xh[t] = (xh[t - 1]\n",
    "              + kappa * (theta - np.maximum(xh[t - 1], 0)) * dt\n",
    "              + sigma * np.sqrt(np.maximum(xh[t - 1], 0)) * np.sqrt(dt)  \n",
    "              * npr.standard_normal(I))\n",
    "    x1 = np.maximum(xh, 0)\n",
    "    return x1\n",
    "x1 = srd_euler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "uuid": "93283652-414e-4773-99ca-00e0b24cc088"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/nT4B0MzMBpJajcPMzBLnxGFmZgNx4jAzs4E4cZiZ2UCcOMzMbCBOHGZmNhAn\nDrOSSHq+7hjMRsGJw6w8PinKJoITh1kPkq6VdGXH8hZJ75d0h6T7ixvfbOjyujdK+mzH8vWS/nXx\n/FxJWXEV0s93XNbarDGcOMx6+ySwsWN5I7ANuDwifhp4E/C7PV571N5HcbHF64G3R8RrgRuAD5YZ\nsNkoHFd3AGapioh5SS+XNAWcCjxDfh+LD0v6GeAQ8COSTo2Ip/t4y7OAHye/78HCjXO+WVH4ZpVx\n4jBb2s3AvyS/Be0ngV8EXkZ+EcVDkr4BnLjoNQc5cm9+4e8CvhYRF1Qbslm1PFVltrQdwDuAt5Mn\nkVOAp4ukcSH5ZawXLNwMaB9wtqTjJa0GLiraHwNeLul1kE9dTeqNlKzZvMdhtoSI2C3pZODJiGhJ\nuhH4rKSHgPvJ72F+ePXiNU9K2gF8DfgG+aXMiYgXJf0L4HpJp5DfQ+E6YPfoPpHZ8HxZdTMzG4in\nqszMbCBOHGZmNhAnDjMzG4gTh5mZDcSJw8zMBuLEYWZmA3HiMDOzgThxmJnZQP4/IwKn8WoHTtUA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6fc05c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x1[-1], bins=50)\n",
    "plt.xlabel('value')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: srd_hist_Euler\n",
    "# title: Simulated square-root diffusion at maturity (Euler scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "uuid": "59c2b6b1-7c7d-44bd-8ae3-8ad16dd2eb30"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hEB/s+qBKWK0cEeGj7z9iTLcxDPAbUOWeq5Mr/h7+v5vFeypWbUPZwoayRdNo\ntQ4Dqk2tvcYZKxp9zw8jKi3KNlvIywtz926EpMPquNUV8p/v+5z2bu2Z3n86bm6BABiNKYzz8gIg\n/PbbK8JSNdiwQXcaM2dy881wgKGYo6uOMHJzd+Lm1pvrrstl6NCdBAa+hatrIOfPf0dc3H3s2zcc\nq7UUTdOYFDSJ7XO2Y3jQQL8O/Xh609P0+KAHLxteJqPQNjLZlbaLU7mnaowuyunh1aNi8Z5CoVA0\nlt+NwwgI1BeKtz8USqGpkJhztg9wp9ChjMxy4+f4nwFbsntO6BzaOLXB1TUI0B1Ge2dngj08CB8x\nQj9s6Ugt24T8+CP4+cH119O5M5z1D8U3PQ7KdrsVsZKbuxMvr+twcGiDl9dYevZ8npCQdYwbl0X/\n/isoKTlBRsbPFU1qmsaEgAkYHjSw60+7GB8wnte3v07PRT15csOTnMg5wZf7v8Sjrwd3DbqrVrv0\n9O55WUcYJpOpSWd9NAYVq7ahbGHjcttCRJg5cyb33HMPmY04+vlKoVU6jMBAfURQxWEE6D/b7B0G\nVF3AR0gIgeklxJzYw6ncUyyNWYrZaubhYQ/rddp0BxwpLk4GYLy3N5GenpicnWuGpYqL4ddfYfp0\ncNJ3XnG/dihOWCjYrTuXoqJ4zOZMvLyuq6G7pjni738vrq5BnDnzaa3PN7rbaFbPWs3Rx49y9+C7\nWRy9mF4f9WJF7ApmDZqFZxvPWuv1aKcv3rtUH9qVSUtLo1OnTixZsuSS961QXCmEh4fz008/sXLl\nSkJCQtiyZcvlVqlR1OkwNE37VdO0tXW9LqWSjcXb25t27dpVWYvRvTtomlCY34MA1wC2pW6zVQgO\nxsFiZUAG/Bz3M0v2L2FCwAT6tu8LgIODE66u3TEa9fbGe3lRJEL0rFnwww9Vw1K//QaFhXDnnRVF\nfe7Uj/g49r2ex8jN1Z2Vl9e4WvXXNAe6dHmM3NwdFBTUvR5jgN8Avrr9K5KfTObJUU/StV1XxljG\n1Cnf07snxeZiMosv/Teb559/nqysLL7++uuGhZsBFau2oWyhY7Wa+OWXf12WL0zlvPvuu/j5+REZ\nGYmXlxeTJ0/mmWeeoaTEvlmQl5v6RhjvAu/V87piqW0thosLdPaHdNpwk+kmNiZtJL0gXb8ZEgLA\nlOKuLNyxkOTsZB6+5uEqbbq6BlU4jOu9vQEIv/XWmmGpH3+E9u1h/HhIT4enn2ZoQBa5tCN3ux4G\ny83dgbOFevfNAAAgAElEQVSzP25uvet8hs6dH8LBwZXTp//d4PN29+rO+ze/T8q8FHr71t1m+VqM\nSx2WioyM5Ntvv6V79+5ERUVx6lTznSioUNhLevpyUlKeIydnW8PCLcDRo0dZt24dTzzxBGPGjCE6\nOprHH3+c9957j1GjRnH0qF3H/lxW6nQYZaurw0UkHNgDnKtWdkVT21qMgCCNDDd3ph2apm+fEbNU\nv9GnD7RpwzRjDy4UXaC9W3tmDJhRpa6ra2BFSKqjiwsD3N0JDwoCTbOFpYxGWLsW/vhH/TjYQYPg\ngw9wfvsNTncYQtukGEQgJ2cH3t7XoWl1b8Dr7OxLx473kJ7+DWaz/Uer1hejLV+LcSmn1lqtVubN\nm0fXrl1Zu1YfmP74448t3u/ljlVfSShb6GRnGwgNhfT0hg9Cawnee+893NzcePxxffcjd3d3/v3v\nf/Prr79y5swZhg0bxqeffnpZR0AN0WAOQ9O024AYYGPZdeiVHpIC3WGkpKRUMX7PnpDu6Eb78PZc\n3+N6luxfglWseq5h0CD6nyyF92Bc8TjaOLWp0p6bWxAmUzpmcz6g5zF2Go2YJ0ywOYzNmyE/HxIS\nYNYsCArScxkbN8KgQQwoPUjsgVRKSk7UGY6qTJcuj2O1FnLu3PJmsUnFCOMSLt5btmwZ0dHRvP32\n24SGhhIaGsqquqYjKxQthIiQm6t/z83I+AmLpeiS9n/27Fm++eYb5s6dS4cOHarcu/XWW4mNjWXC\nhAn89a9/5auvvrqkujUGe5LeC9BPzssBEJEYILAFdWoWRo0aRUFBQZVvswEBcK7IGWO6iTk953A8\n+zhhqWH6zeBgnGLjIB9803xrtOftPR6A48f/Duh5jAKLhQOzZ0NcnB6WevddfcSxeze89RZERsJT\nT0FJCT26WWlLIYkb9ZlPtSW8q9Ou3XA8PUdy5oz93zrqileLWPF188Xd2f2SjTDy8vJ44YUXGDNm\nDPfeey8Ad955J7t27WrxsJSK29tQtgCjMZWSkjRSUq7HYsknM/PXS9r/xx9/jMlk4umnn671fqdO\nnVi/fj0jRoxg4cKFmExX5iah9jgMk4hUj4lcuWOmMmbNmkVwcDDPP/88paX6fkw9e4LZqpFJGyae\nm4iPqw9L9uuzdtI7dcK7qIgOwIHompsFenmNpXv35zh79nPS0//L+PI8xujRupOYOhW2b9fPEj9w\nAJ5/Xh+5jB0LnTvT9kwiAG2ObsTR0RMPjxC7nqNr179SVBTfpLjriRNvEhnZhZycMHp69bxkI4yF\nCxeSnp7ORx99VBF+u7NsMsBPP/10SXRQKAByc7cD0KnTA7Rp0+2ShqUKCgpYvHgxM2bMoFevXnXK\naZrGyy+/TGpqKt98c3nCZg1hj8M4omnavYCjpml9NE37GIhsYb2ajKOjI//6179ITk7m00/16ak9\n9RA+513cKN1Tyv0h9/Nz3M9cKLrAZxH6ed8vTJvGoUOHKCqqNmTdto2g54/T+eQQEhIepp05hT5u\nboRbrTBxIpw+rct9/bWeuyjHwQFmzIDISMwOzvTMPoCHxxgcHOw77NDP7y6cnNpz+nTtU2yrUz1e\nbTSeIDX1NczmTA4enMztXeDkJXAYiYmJLFq0iLlz5zJ8+PCK8j59+jBkyJAWD0upuL0NZQvIyQnH\nyak9t9wyl44d7yUra2OV7Xhakq+++oqcnByeeeaZBmWnTZvG0KFDeeONNzCbzZdAu0bS0AlLgDvw\nBvphSHuBhYBrY09qaskXlU7cq4zVapXJkyeLr6+vZGdnS1ycCIi8MSBV9obulUPph4QFyLyV86Sj\nPjlWDv35zwLI9u3bbQ19952Is7OIpomAnJvSRg6s7yePxB0Qr+3bxXz+vMidd4p4eYmUlNRUJCxM\nBKSoU3fJHIFs2PB6rfrWRVLSs2IwOEpx8alG1RMROXLkXgkPd5WCgsNy8OA0MRiQ+d+7isVSi57N\nyG233SZt27aVs2fP1ri3cOFCAeTUqcY/j+Lykm8yyZPHjsnRgoLLrUqj2LUrSJYufUH8/ETi4uLE\nYEDS0j5p8X5NJpMEBATIuHHj7K6zevVqAWT58uVN7n/dOpG6/s24iBP37PkwvqaxjV7qV10OQ0Qk\nJiZGNE2Tv//971JYqD/xM5OyxIBBStJLZMx/xoj7s+7Swa+DWPz8pOieewSQd999V2/ggw/0Stdf\nr1v++efF6uIsJjfk6JNDxOW33yTmwgURb2+RBx6oXQmzWcTfX4oH+UmJD/Lyy2F16lsbRUXJYjBo\nkpz8YoOylY+gzM2NEoOBinpWq1lWGK4XgwGJ3jdWSkrON0oPe9m4caMA8vbbb9d6PyEhQQBZtGhR\ni/Qvoo7irExz2uL79HTBYJCOO3fKkavEaRQXnxKDAZk7d7+AQRYtEtmzJ0T27Rvd4n2vXLlSAFmz\nZo3ddaxWqwwZMkT69u0rZrP5ovvet0//6PLwEHn3XZHS0qr3L8Zh2BOSek/TtDhN017XNG1wMw5u\nLglDhgzhgQce4MMPP+T8+VT8/CCjrQcA2VuyubbNtRS5F3Hvc/fiMGQIbomJBAQEsDsqCp57Tk9a\nz5ihL8jr1g3eegvtyFFKxvVlwEcHSZk7C9PLL0NODsycWbsSjo4wYwYFPpm4ZMOWFd1pzMw5N7dA\n2refxpkzS7Ba7TsfQ0RISnoaF5dOdO/+HKCvIsf3L7x+FPLzo9m3bwQFBTXPAWkKJpOJp556it69\nezNv3rxaZfr27UtISIiaLXUVEpGbi5uDA46axoSYGA4X1NwE80qjPH8RFdUf0Ddi8Pe/j7y8KIqK\nklqsXxHhnXfeoW/fvtx2221219M0jZdeeoljx47xww8/NCi/YcMGtm/fXqN86VJ9/dn48fDMMzBs\nGJRF3i8ee7wK0Al4EogADgEvNtYzteSLekYYIiKnTp0SV1dXuffee2XECJGbJltlh+8OOfLgEQkZ\nHiLafE3uXXWvyFNPibi5yeyZM2WVh4funh99VB8hVMNqNUvi4iGS31MPU4mnp4jRWLcS27ZJwjw9\n7HUL6yU+vl6Va3DhwnoxGJBz576zSz49/QcxGJAzZ/5TpTw8NVxYgGw++olERHSV8HB3uXBhXeOU\nqYdFixYJIGvXrq1X7vXXX1dhqauQYXv3yoQDByShsFC6RESI386dEpuff7nVqpf4+IdlzZreAiI+\nPiJOTiLnzqWJwaBJSsqCFuvXYDAIIJ9//nmj61osFhk0aJAMGDBALBZLnXLLly8XTdPE399fSiqF\nw41GEV9fkbvuErFaRVavFuneXf+oeughkYyMixthNPaDORhYAZQ2tqOWfDXkMERE5s+fL4DceGOm\n9O0rcvjOw/Kqz6t62fs3iutCVyn4/BMRkDM9eoiA5P3977q168BoPCvrt7aXqKd8xfTNV/X2bzbm\nyY41usN4gTfkgw8aVLkKVqtFdu3qJfv3NxwLtViMsmtXoOzZEyJWa1Vnl5qdKixA/rPvP2I0npE9\ne4IlIqKrWCz1ODs7yczMFB8fH5k8ebJY67GbiEh8fHyLh6UUzUu+ySSOBoP84/hxERE5VlgoXSMi\npMPOnXLwIp1Gsdksn50+LdnV4yXNyO7d/eWf/3xbwBZhXrlS5MCBiRIV1bvB9+rFMnXqVPHz85Oi\noqKLql8ezvrhhx9qvf/DDz+Ig4OD9O3bVwD55ptvKu799JP+nOvX2+QLCkSefVZ3mL6+LeQwgAHo\nazEOA2HAY0DHxnbUki97HEZubq74+flJt27fiaurVZI/TZEudJFBfQdJdFq0sAD5bunfRUCsDg7y\nZzvjjt8l/ShbDA4SGXtPvXLZ2WFiMCBmV+S3tjPk5psbbLoGJ0++KwYDkp9/sE4Zg8EgJ068IwYD\nkpm5ucb9UnOpOLzqIC9te0lERDIzN4nBgJw+/VnjFarGU089JQ4ODhIbG2uXfHBwsIwdO7bJ/daG\nymHYaC5bbM3KEgwGWX/hQkVZYmGhdIuMlPY7dkhMI53GGaNRRkZHC5WcUHNTUnJODAbk7rtjxMtL\nZNMmg3ToIDJ7tsiZM1+JwYDk5u5u9n4PHz4sgLz22msX3YbZbJb+/ftLcHBwjVHGr7/+Kk5OTjJu\n3DjJz8+Xfv36yciRIyvu33abSOfOIiZTzXYPHRK57rqLcxj25DC+ArKBm0RkgogsFpHzFx8Euzy0\na9eOV155hbS0nRiNGt+mbuEMZ3jm+mcY1nUYw7sM5+389cjcuZR+/z1LnZzYvXt3g+2O6jKVb5lN\nSeZ3ZGeH1SlXvuGgZoZR1kjCwvQjMxpDp05zcXBw5ejRu8nONtQqYzLlcOLE6/j6TsPXd1KN+86O\nznT17FqxeM/HZxKenqM4efKfWK0Xv1jo+PHjfPLJJ8ydO5fg4GC76tx5551ERERwunxKsuKSkp+/\nn9OnP7U7LxaRm4sGjGnXrqKst7s7YaGhuDs6MjEmhpj8fLva2p+fz8j9+zlcWEhvNze+z8go//LX\nrOTklOcv+jFhAjg7w7RpsH49+PjMwMHBtVnXZFitVlasWMFNN92Eh4cHjz322EW35ejoyIsvvsih\nQ4dYs8Z2IujmzZu54447GDp0KOvWraNt27Y88cQT7Nmzh927d5Oerj/f/fdXbJhdhcGDIfxiN3ey\nx6sAbkC/xnqjS/XCjhGGiEhpaal06fKIgIiv7xQJdQuVmFtiRETk8+jPhQXIrlO7RETkmmuukYkT\nJzbYptVqlaAIg/wS3lX27BksFkvtQ+uYmJtlz+5BIu7uIiBtyasyXLSXCxc2yK5dAWIwIIcPz6ox\n1TYh4a9iMDhKQcHROtsY++VYmbB0gn7x2GNS8MrcsnzH141XqIyZM2eKu7u7nDlzxu46cXFxAsiH\nH3540f0qLp79+8eJwYDs2RMieXn7G5S/OSZGBu/ZU+u940VF0iMyUtzDw2XesWOSWlxcZzur0tPF\nLTxcukdGyoG8PFly+rRgMMi+vLyLfpa6OHbsCVm5coCASPnb7Mcf9dhKWJjI4cN3yc6dfnX+3zaG\nqKgoGTVqlAAycuRI2VOHrRqDyWSSPn36yJAhQ8RqtUp4eLi4ublJSEiIZGZmVsjl5eWJp6enzJ49\nW957T3++I0fqb5sWCkndBiQAKWXXocDaxnbUki97HYaIyKJFW0VfcnGnfH/H9xLuHi4Wo0XyjHni\n8YaHPLTmIREReeyxx8TT07PehFM5c+Li5KbwN8VgQE6erJmcsFrNsn27pyQkPCZy880iILe4bJW/\n/c1utatgNhdJSsoCCQ93lfBwd0lNfUssFqMUFBwVg8FREhL+Wm/9e368R4I+DBI5dUqsmial3t6y\nwxAsUVF9auQ87CEiIkIAWbBgQaPrBgcHN2qOuqJ5KC4+IQYDEht7u0REdBKDwVGSk1+sM5dltlql\n3fbt8kg9szVOFBfLA0ePilNYmDgaDHLf0aNVEuJWq1VeTUkRDAYZs2+fnCtL0maWlopTWJg8m5TU\nvA8pInv2BMuCBe8KiBw+rJfl5Ym4uIj8v/8nkpGxVgwGmjTxIy0tTe6//34BpHPnzrJs2TK7Pjfs\nZenSpQLISy+9JG3btpX+/ftLenp6Dbl58+aJk5Oz9O9fKpWiU3XSUg5jH+AFHKhUdqixHbXkqzEO\nIyfHKiAyYsQqyVibIQYMkrUtS0RE/vzLn8X9DXcJTw2XRz95VBiHzFw2UyYtnyRBHwaJ55ue0v39\n7hL6WajcuOxGuWvVXfLor4/KzF+fElZ/INuib5Tt29uJ0Vh1sVpe3v6yGU7finz7rQjI+m5/kT59\n7Fa7VoqKUuTQoeliMCBRUX0kOnqUfPihR4PrK57f/Lw4v+YspW++IWXeUyZrmnTvjkybNlIWLFgg\nP/30kxy3I65stVpl9OjR0rlzZym4iHn5r732mmiaJqdPn2503fpQOQwbtdnixIl/icGAFBYmSmlp\nphw9+kDZaGOw5OburSF/MD9fMBhkeS0LMcsx5ZokJzJHThYXy1OJieIRHi4YDDL14EHZnJkpdx0+\nLBgM8sDRo2Ks9oE65eBBCdi1q1kT0KWlF8RgQG6//ZD4++vzV8ptcfPNIn37ilgsJbJjR3s5cqT+\nHGRtmM1mefPNN8XDw0NcXFzkhRdekLwWGCWVlpZKUFCQANKrV686/1eOHTsmMFRA5NNPG273YhxG\nq91Lqi68vDS8vYURI2biPcEbzUkje1M2AA8Pe5giUxHjl47nswufwSTYdGIT+SX5jOw6koeGPsSN\nQTfSvV13is3FHDx3kB/jfuTn/R9C3EI2uj6D1VpMcvLzVfrMzd1R1vd1+loNTWOMcRuJiZCYePHP\n4uYWwODBPxMSshHQyM/fjb//fbi4+NVbr4dXD0xWEzmf/psDQImLC28OHUqvXp4cPBjDq6++yh13\n3EGvXr145JFH6t0IbdWqVURFRbFw4UI8PDwa/Qx33nknIqL2lrrEnD//HZ6eI3B3742zsy8DBiwj\nOPh/mExZ7N8/muTk+Vgsxgr5iFz9I2Bs2Zn2tRH/UDwHrj2A86oc3u/dm5NjxrAwMJC9+flMjo1l\nVUYGbwcFsbR/f9o4VP3omdWxI6lGI3vszIHYQ27uTkQgKqovEyfqW76Vc9ttcOwYJCa60LHjLC5c\nWFOxE7W9LFmyhPnz53PTTTcRFxfHm2++iadn7add2kNJCSxcCBnVdixxdnbm/fffZ+zYsWzdupUu\nXbrUWr9Pnz707LkAMDJjhn15qUbTkEcBvgTuBWKBPsDHwGeN9Uwt+aIRIwwRkaFDRcaP13/ff91+\n2TvM9o1qbfxaWRu/Vg6ePSjtOrSTRx55pMH2lsUsExYgfhu+kqSk58RgQHJyIiruHz48UyIje9oq\ndOkiVgcHaUOxvPlmo1SvE4ulRDIzN9sVUlp3bJ0MfEwfWbzZubNY77lHpH17OZe2XAwGJCXlW9mz\nZ488/fTTAsgNN9xQJV5ajtFolMDAQAkJCWnSitTBgwfLddddd9H1FY2jsDC+LHz6fo17paXZEhen\n57QiI7tLWtq/xWwultlHjkiniIg6RwD5B/PFgEG2e22XMKcwydxke78Umc3ynzNnZFMt76Fyckwm\ncQkLk6cSE5v+gGUkJj4ly5aFCIgsWVL1XmqqPrh+5x2RnJxIMRiQs2eX2d12UVGRdOnSRa699tpm\nGxW9+66u08svX1x9o1HE07NE4LsqU2zrghYKSVXeSyq67PerYi+punj9df3JExJEUl5PEYNmkJLz\nNfdWmjx5soSGhjbY3vmC86It0ISv58jurDMSGdlN9u4NFavVLFarVSIiOsmRI7NtFWbOFAF5tu/P\nEhLSKNVFsrNr36+qERxKPyRvDEJMIN8tWqSv6gGx/rZBoqL6yN69Qyv+CZYvXy4uLi7Su3dvia8W\nv3733XcFkE2bNjVJn1dffVU0TZPk5OQmtaOwj+TkV8Rg0MRorDsMmJW1Vfbtu1YMBiQioqv8acfT\ncldszVBVOYfuOCTb222XopQi2ROyR7a33S55+xsXnrk9Nla6RkSIpZk+gPfuvUaefXaRgEht0dUh\nQ/Qdf6xWq+zaFSR79gyW7OxwuxzA+++/L0CzhT6zsvRFhSDSq1e9y7/qpHztRdeuf6oyxbYuWsRh\nXA2vxjqMc+f0vQTnzRPJjcoVAwY59925GnIvvviiODo6SmFhYYNtjlgyWnivn7xw/Likp39ftrnZ\np1JYmFhzncPy5SIgxwfdKiBytO4JTVU5f16kY0eRekY99ryBc4uyJcUJ2ezsKEajUaS4WKRtW5E/\n/7libvqFC/+rkN+5c6f4+fmJt7e3bN6sr+24cOGCeHt7y5QpU+xUvm5OnTolbm5uMmvWrCa3VY7K\nYdiobAur1SpRUX3lwIEJ9dYpPFYopdmlkpW1RaKix4rBgGza7icnT74vZnOhWK0WMRrTJDt7u6Ts\n+UwMc++XPd/dLgkJf5XiU8US2T1SIjpFSFGK/YvW/nvunGAwyPbs7It91ApMphwxGBzkppuOSECA\nrbyyLV58UcTBQeTCBZH09O9lxw7vsjxOsKSlLRaTqfZ1Jfn5+eLn5yeTJk2qs3+jUSQtzX59n31W\n39t03jz9U3n3RSwNue02kS5dRD788BMBJCoqql75ZnUYwK/A2rpedncAtwDxwDHguTpkPgIS0U/2\nCy0rawPsBg6gb0fySj19NNq4s2eLtGsnkpdjlR3eOyTuobgaMmvXrq3YuTZzU6YcmHig1pGIiMgb\n298QFiC9w9eJ1WqVAwdukB07fCqSiwUFlea4HT0qAmJxdZU2GOWVV+xU+oEH9D+Zm5s+0qgFez4o\nE7/+WgRkwbhetsLZs0V8fcViLJTIyJ4SHT2qyjetlJQUGTRokDg6OsrixYtl3rx54uDgIIfLp540\nkVdeeUUA2blzZ7O0pxyGjcq2yMvbV/YFpu7tKjI3ZkqYS5hED48WS4lFfkhPlyGGDyR873ViMCDb\nt3tKWFgbMRiwvbY4yM4d/mIwIBkZa6XgSIHs8N4hUf2ipPSCfVNW800mcQsPl78mJDT1keXChXWy\nZYuDeHmVykMP2cor22L3bv3facUK/dpsLpQzZ/4je/cOrXjOY8eeqDFFvXy35d11fKobjSLjxom4\nuorYs4b15EmRNm1E7r9fJCdH/33evMY977lzIo6OIs89V3WKbX00t8MYX9/Lrsb18zaSgJ6Ac5lD\n6F9NZgqwruz3UUBUpXvuZT8dgShgZB39NM66IrJrl/70ixeLHJ55WCK7RdYYiqanpwsgb7/6tkR0\nihADBol/uPZphQfPHRQWIPz3GYkrKJCCgsMSFuYkYWHOsmOHr1itlWaFmM36uwJkWc8XpX9/O4ag\nW7boCt9+u/7z448b/czlbO3bVwpB/vjRjbbCNWv0dn/7TdLSFpetFK8aasrNzZWpU6cKIJqmycMP\nP3zROlSnoKBAunbtKsOHD2/WKYmKqiQlPSNhYc5SWnqh1vvZ4dkS7hYukT0ixYBBjj9/XOYdOyZu\n4eFSarFIdvZ2iYv7kyQl/V3S0hZLWvQaMXT5Ro6/HC8Wi0l27Qqs+LKRvT1bwtqEyb4x+8RcZF+O\na+bhw+K/c6eYmxiWSkp6Tj7/fKSAPjGxNiwWkU6d9P2WKmO1WiUnJ1KOHr1PwsJcxGBAUlP1ZGNW\nVpZ4eXnJH/7wh1rbtFpFHnxQ/1fy8hIZMEDfkqM+5szRp/mmpurXM2aI+PvXvkq7LsrXXpRHK+bN\nmyfOzs71rou64kJSwGhgQ6Xr56uPMoDPgFmVruMA/2oy7mX5kxF19GO/ZcuwWkWGDRMZNEgk7bPT\nYsAgBXE1/7IBAQFyc4+bJcwpTGJvjRWDZpC8AzVjs1arVbq+3134eJy8VfaXT0x8umyuey1vrlGj\nRDp1EqumyWR+k5iYsvKMDD0YuXGjTbaoSKR3b/1VVKQrPnjwRQU6Tx0/LhdA1nbykJDFlRIoxcX6\nBop/+pNYLEaJiOgi+/dfX6O+2WyWp59+WoKCgmo966IprFixQgBZtsy+5GNOzk4pKakZSlTUjtVq\nkcjIbhIbe2ut93N358r2tttl94DdUnK+ROIfjheDZpBZi6Nk/P7aF/aV5y5KM/VRxOnTn4nBgGRl\nbRERkfRV6WLQDHLoj4fEam74/bqqbPv0rVlZF/mUOvv2jZYnn/xEQKS+taR//rP+tq8rLVhSki4b\nNjwq69d7SX5+jMyfP180TZODB2vfnuef/9Q/VRcs0L/jaZruEOoiNlaX+X//z1ZWnouwNzW47MxZ\n6d7fJKNG2cr0KbbIK/WEL65Eh3EH8EWl6/uAj6rJ/ApcW+l6C2VncJSNUA4AecBb9fRjn2WrURaZ\nkQ3fGsWAQU59WHPn1D+O+6P44y8pC1KkNLtUdnbYKfuv219rYuzx/z0uDq+7yfDd+gwpkylX9u4N\nlXPnapmx8OijIt7eYurdT3LxlH2DHxAZOFDK10WIpomsWqXL/uMfetkW/Z9QvvhCv46IqNFsQ6GY\nr2fMEAF578mJ4v1P76o377tPz7yVlsqpU4vEYECys8Prba85sVgsMmrUKOnSpYvkN7AvkX5GiKMc\nO1b76kcVkrJRbovs7O229UDVyI/Jlx3eO2RX0C4xntYX75kLzLKrf5Ss6mCQV/Yeq1mnbGZU8ku2\nyQrlXzYq50hOfXhKl3u54UkNhWazeISHy8ON3c65EmZzgYSFOcl11yXIwIFV71V/X/zyi/6vtLnm\ntmtitYp88omIk5NVunRJkY8+uls8PDzk7rvvrrXf1av1f9u777Z9l3v5Zb39ur4DTZumH6VTeQJZ\ncbE+OnnwwYafNc9kErcl+yqiJZWZOnVqjV1sK3MxDsOedRiXDRGxishQoBswStO0gXXJzpkzhwUL\nFrBgwQIWLVpU5eD7sLCwWq9nzYL27eHNz3ZxtMtRsjZlVblvyjTRPaY76aQTPSAaZ29nAt8IJHxH\nOGsW2PZ2+fzzz1m0aBG39r0Vq6WY6I3LWLVpE05O7Rg+/ABxcV1r9u/mBjk5OCUlsJ98sg9/g3Tv\nDm++SdiHHxI2cCDcdx+sWEHYW28RNnky3HijXr9bN73+Z5/V+3zVr/Pz8/H89VfWOTmRGNiLHGMO\neSV5Nvm77oLsbMI++ICEhH44O/uTmrrA7vabeu3g4MCiRYs4c+YMjz/+eL3yq1bNAywUFh6p9X5M\nTEyL63u1XMfExBAWFsb589/h4ODG4cM+Ve5vWL6Br8d/jaOnI0O2DmHXsV2EhYXh6OFI8WfdSMmO\nwfOvhvIvZxXtp76WimM7R44PP17RnoNDG9LSphMWFkZurn6Sc1JIEkmhSWT+mtmgvu6OjoxKTmbl\npk2YrNaLet516z5j715h374gJk6sX37SJHB2DmPx4qr3N20K4y9/gSeegNDQcEpL45g3bxlFRX9h\nypSpNdpbsiSM2bNh5EiYMyeM8HD9/ssvw5AhYTzySBjx8VX7Dw+HdevgrrvCiI21tRcVFca114bx\n8715qnIAACAASURBVM9QXFy//t+dP0/xsuPguI2J00ur3H/yySdJT0/n5ZdfrihbsGABc+bMYc6c\nOVwUDXkUaplCC3Swxxuhh6Q2Vrq2JyQVT7WQVFn5S8DTdfTTsCuug+ee02dKGO4/LuEe4WIpscXP\nj9xzRD5x1GcclO9cazVbZW/oXonsHinmQrPEx8dL27ZtxcvLSzJzM8VtobvwxXT5d0NTJNLT9Y3p\n331X9v3xVRGQ03Pm2+5nZIj06aPvReztrc+Qqsxjj+l5kHrmtlfnk7fekkKQc3fcISsPrRQWIIfS\nD9kEjEZ9JsDcuSIicvLkB2XhBYPdfTQH9957r7i6usqJEydqvW80ppXFljWJiOh8SXW7WrFYSmXn\nzg5y+HDVmWhFx4skokuE7PTfKYUJNWcDvp6SIjMfN4gBg6Qttr2naxtdlGM2F8jOnR3k4MGpFWVJ\nf0+SMJcwsZQ2nJ9ak5EhGAyysRHv7cokJ78oH354vYDIzz83LH/rrSKBgbZRwenTIqNH6yODF1/U\ncx2xsWmiaWsERKZNy6vyb3f6tEjXrvp5E7VFadPSRDp0EAkO1iPKInpfI0eKdOtmK6tMecqyjp3N\nKxi0Ovb/s/fdcVFc3ftnCx0bNhSIvQv2FkuIsfeavBproqgxMbZYYgm2WKJibLH3FjUaY49llt4R\n6VUQUUCqIG3LPL8/7u6yyxZAQ75v8nufz2c+yuydO7OzM/fce85zngMyVYCGpOFauTFCoVCgS5cu\naNKkCYr1aHtRNeVhhBNRb42/JxJRXKU6Z8FqVdDblFjQu125NiOoLOjdm5RBbyKqR0S1lP+3ICIP\nIhph4DzG76oRJCUxg7F4UiE44pArYeyj19degyMO0euiIRaLsXr1avUxue654IhD5PeR6NChAyws\nLEBEOHnyJMZcGAPxNlt88uRJpa8hJwc4Jpij9I/dLftAlTBSvz6jQWgiNJR9VsnCGjKZDIuZCD7g\n5QXfF74gV8Kt2FvaDadPZwaqtBRyeRG8vRshJGRAtdUM0IeUlBRYWFgYXPrHxy8Bx4kQEzMPHEeQ\nyfL+tmv7pyIr666SwVQm2V/8ohi+zXzhaeOJgnD9LsBhT5+io68fQoeGwt3cHW8jWZyvfOyiPJKT\nt4DjSC1qmH4uHRxxBs+jiRKFAjU9PDA7Wpe5WB48z4PnFeB5ORQKGRQKKUJC+sPF5RAEAvZuVYTD\nh9lrER7OyDCNGrGyplevlrVxcXGBWGyC2bO/g1gshYMDDy8voLAQ6N6dtVfHIfXg7l12DhVP5PJl\n9vcJA2V05HJ2HePGGe4z8E0+qGcWzKwVML3qg2V6kh4fPHgAIsKuXbt0Pqsug+FILGnvJyI6T0T3\niMi+0idgtNpYYrTZVcp984jIRaPNfqVheUpl8QtHIgpRGpkwIlpj5ByG72olMHYsUK8uj/tCdyR+\nn4jSzFJ4NfBCYNdAKKQKvcq14ZPDMUQ0BAKBAPfv30fbtm3Ru3dvHAk6AnIliG6dQE4VisJMHFGE\nKBNH8PXqsdrhr14xR2a3bkzhtnt3XbpFr14oT7Ey5Lu/ePEi7hHhbYMGAM/jZf5LkCvhYEA50Zmb\nN9ljoZTSffHiZ+Uq41Glv8tfgfXr14OI4F0uTlNamgl3d0tERU1HZuYNZT0DXb75/2IYZeA4DlFR\nM+DpWVtLXPDpiKfwqOGBN4Fv9B6n4HnU8vCAS0wMStJK4FXfCwFOAXgT8Mbg6kIFmSwPHh61EB4+\nEQBQEMZWJOnnK0dSmBEVhdqenijVYMyVlmYiI+MSoqO/xMmTDXHokAatt9zWvXsiunXTfy/K4+VL\n9sh//DFjKzVvzoyHCgkJCRCLxVi4cCHS0k7j0KFu+OCDPIhETDVCIGCxkIqwciU7z5kzjL/SsaPe\nYp5qLFnCrseQ0Ru0JxVEwNZdcvQNDkbv4GC97YYMGYI6deogp1xH1WIwWL80jogKiOgVEbWs6kmq\ne3tfg/HgAbsTG1slIahHECL/EwmJiQQFYWw2pE+5dv9W5qpa2JEpw6oyP//0+5PRa0/PxdkqsIjO\nnQNaUwzkFlaMxD1pEnM5xcayQVwoZBEyTa6dKmovkah36XsheJ7HECcnyInAK1dKCl4Bk40mWPVg\nlXbjkhJmqJTUDrm8WMmY6ve3rjLevn2Lxo0bo0ePHlr3PTFxDR4/JsTFcbh79wxu3iSkpZ3SOf5/\nBqMMDx/eg4dHDURHlyUkvAlkg37yj8kGjwtTCg6eVj7HWbezmPxHDQ+jqwsVEhPXgOMEePs2Cgqp\nAhJTCRJWVE6R9nZWFoh7jNvJN5CY+D2CgrqD4wTgOML589awtBSjfn1rxMWtQ1KSK5KSNiApaSOS\nkzcjOnoXTEx4rFih26+h56J7d/YqDRmi6+WdNm0aLCws8OrVK/A8j6dPh+H2bVtMnFgAImDHjkp9\nJUilQJ8+zMAQAbduGW8fGMjalZc1AYCXOTII6pfApl0xZDJgZUICTCQSFOmxQE+ePIFAIMCKcjek\nulYYx4lV2mtGREOVMYaFVT1RdW7vazB4HmjTBuhkx9hSHHFI2pSk/lwlLxypFJgPCgqCqakpBrQY\ngEf0CLnuucjOzoaZmRm++uordD3cFSZ7nDBBc5pSAfLzWaLPycFMzZZZMI1qXb/8AvWaVqFgvrTf\nfmMHNWsG9OjBSOVz52pPjwBIJBIsUvWpIZLfwq0ZHn3SAhgzhmUvvVHONGfMYEZDya5ITd0PQxX8\nqhNnzpwBEWH9+vXYvXs3vvhiBjp0EKFGDRMQEYgI48YJkZCw8m+9rn8aXr++qvP7hY0Jg2cdT8je\nGCb7/5KaCuI4JGg42eMWxVW4ulBBczUIAIGdAxE61IjfRvNYhQJT3RcrVwwiBAf3RVLSBmRkSNC1\naxeIxWIQEW7omdrfu8cedU1mekWQSJh3t3zug7u7O4gIK1eWPWPFxc/h4WGNJ08GISmpapOo588Z\nEfHjjytmxfM8U9R1dtb9bJBLAUjA48gDNqn9Qxn3cTeQ0Dtt2jSYmZkhJSVFva+6DMZiIhJo/F2L\niI5X9UTVub2vwQBYHhwRcJCC1K4oFVSFfk6cOIGcnBw0a9YM9vb2SH+eDh8HHwR2DgQv5zFt2jTU\nrFkTq+6vgmCDEBYPbui1+IYwcSJL2FEs+w58/4/YbF8Tq1axizQ3LzMqqm3AAGDy5LLPBg4EbtyA\nQipFr169ECIWQ1FOuOrgZy1Y23r12L9mZsxp+h0rVauaAikUJfDxsUdwcJ+/dZWhUCjQs2dPtXGw\nsbFEp06EL7+cjP3796Nv376wtzdBWNjYv+2a/okID58IL6+GamHKglDmHkrakGT0uGlRUWjo5aX1\nmytKFEg7kwZ5YeWea5aLJEJRUSKiZkbBu5EuFVwfeF6BGx5N8AvXAfklZVP+b7/9FkSE3377Dba2\ntnoT6FasYNI/76C2r4WioiK0atUKzZs315HuT009qCw6dqzK/WZksNhHZeDqylYkLzQY/0+fAiTi\nYTM+Q/3bZEmlII7Dj6rsv3JITk6GqakpZmkkhVSnS+pfUXHPGN68AayteYx3ykdhvPavqVAoUKtW\nLbi4uGD06NEwMTGBry+rzJfxawY44hD3TRyuLrwKIsKCMQtAroTJ47/Hg74BeH3NeH0KFa5cAQTE\n4/HgKHBCDt523gjuHYyIyRGIXxaPF7ufo2D6OigWLmK5GF5eLBeDiMluAuB+/x3YupXRL4jwpn59\nbFQZFWUbAICfH2QiAW47WrAVi7c30yNo3LjMCH3wgZr2oXpBsrOrMG37C5CRkQGJRIJXr57pMG9+\n/vlnEBGuXWumc9y/0SX18uURJCVVrUa0TPYGbm4mWvkqEZMimEsp17hLqZmvb5VWyfpQUvISEokp\nYmLmIWVXCjjSL/RZHtnZD8BxhEHc9/hNyf65ceMGiAiLFi0CAKxcuRIikUgrm1mVkGtI/Lgqz8WK\nFStARHj0SDd+x/MKhIQMgIdHLaMiju+LuDjtV1ehAJx6yUG1SrEtTJuJ2c7fHyMNJBQCwLJlyyAQ\nCBCm1CuprhXGv6rinjEsXMiCTHqKWWHw4MEwMWGukL1796r38zyPJx8/AUccHtNjNKEmaCtqC5uV\nNugx+2P84aCUe75XMUWwsBD4VhwPjjhEzYhC9KxoPPnkCfxa+cHd3F3tLgsbVU6gpl8/RsFVKMpe\nCJkM+cePw0csBojACwRlami5uUDTpsixrY06qwSQyjUGDoUC8PRkmgZELMEQqlWGg47G1N8FFcVX\nUzY+MjISRITlywVQKLQHoX+jwfDzawmJxAxyeSWnpwDS0y/Aza3svr2NeMtcSmuNu5RelpSAOA67\nNFwY74rY2PmQSEyR8TACHHHIflDxuxAePhGennXR2PMRPo2IQEpKCmxsbNClSxcmmAkgNjYWRIRt\n27bh9Wtg924WSCaCwbIBlX0uAgMDIRQKMXfuXINtCgvjIJGYIipqWqX6fFf06MGC6wBw7Bj7fiar\nYpBbjlQzJyYGtT09Dar9Zmdno3bt2hgxgk26qstg6Ku4F1HVE1Xn9lcZDKUmIJYu1f1s7dq1ICJ8\n+umnOgOmvFiO4uRiyPJk2LNnD4gIY0+MhcmWGrC//RgBnQLgbuWON3762SgqpOxmM7ClZvEoT7Di\neR6lmaV4tu6ZVpVAACz+oJkJroSLiwtEIhFiLl1A0a3fVR0x35dYjBunvge5EpJyk3Qv5vZtqN1f\nytjGy5eHlUq271CM/D2gL3sYYPfE1rYOnJ3JaA3zfwNUJVWrWk40MnIqvLwaqLXMIqdEwsPao0JB\nwMtKiQ6/N8af2cpAlZUf83QhOOKQstO4ESopeQWJRIyEhOX4KjYW5o8eoU/fvrC2tkZcXFnGuUwG\ndOjwHayt70EsZpU0e/Zk4b4qEBR1UFpaCkdHR9jZ2SEvzzhlOzHxe+VE5q8RzdSHPXvYq+jhAdSx\n4SF0ysPMKF3K8clXr0Achwgjvrjt27eDiMmyV5fBUOVFaBqMsKqeqDq3v8pgACxmLBIB5dMooqOj\nMWfOnApLMObk5MDc3BxDFg1hbKnrbuCiM+Db3BeedT3xNkr/j5lxmWnu/PlhBATEq1itOpAXy+Hz\ngQ+CugeBVygNV3ExYGPDYhhK+Pv7QyAQYMmSJdjsvhn1dtRDbnEuq92oXOM+SHwAciW4J+uR/5BK\nWSYSEXtiwYo0MSXbHgZXGdWx+lDpE+kLuk+ZMhI1axLS06/85ef9b0LaMyYIyT0mxMZ+ValjFAoZ\nPD1tEBU1EwBQGFMITshViqn0bVwczN3dtWit74OYmDmQSEzh1ekyomaUGffS0lKsWrUKR48eRVYW\nE0RMTt4MjiMcPJiOD1rLQbVegCgYLVu+hrMzK686ZgzLU2De0wx8+umL8lyPd8aGDRtARPjjjz8q\nbCuTFcDb2w6BgV0rVbzsXZCWxkiStWsDQjEPOhEAXz2GLK6wEMRxOGyk3HFRURHs7e3Ro0ePamVJ\n/asq7hlDdjbLk+vZ0zhH2hhmzpwJqzpWMN1oCvHxT/FldDSKEorg1dALPg4+KE7RzrpUqXqG9AtB\nUZ68Qh2ZtDNpujU8liwBxGJwe/ZALpOhW7duaNSoEd68eYMOBzqAXAmbLy1kge3hwwGFArFZsSBX\nwpnQM/pPpFKwVeZuAMDLl0e16mXIZG+Qnf0nkpI24OnTYfDkaiDc/aN3u3F6UKaA2lOvMTp16iiI\nCLduaQ+i/yqXVEQEon6sCa9rhKdbCb6PGlbKMOfmeoLjCNeu/QAAiJoRBXcLd5RmVBxD6B4UhAEG\nBAffBSUlL+Hubgnvg0MR0ClAvV/FQCQiiEQiDBkyGKtW2WD69FMgAtq0yQPRZZg3DMDgwYzb0bMn\nK340dixw8WIxrK1tMLMywkuo+LmIiIiAiYkJpkypfI3v9PSLFUrGvy8GD1a+itPT4BgQoPf353ke\nDby8ML2CAjsnT55U33NUg8H411XcqwjnzrE7c+DAux3v4+MDIkL7re1Ra1dTmLu7I7O0FPlP8uFR\n0wPe7b0RGBOIO3F3UBBZAM86nvBv66/mtc+ezRQ0DTEpeAWPgE4B8G3qC0WJcgaYmAjUrQuOCAft\n7EBEuHDiBBKyE0CuBIvNFqi3SoS3H9iqZUaKpEXMkLhvNnAiviyWcf06ACYx4evbDD4+DggIcFRz\n4zlOgADfdgg+JGb1P96833SvtDQTubkeSEj4TpmhrE2fzMpiuYXh4a9ARFi2rIvW5/8ag3HuHHhL\nC/hcFSLi0UdIdbEFxxEKcysutJCYuAoSiRgPH95EUWIROBGH+CUVl0DNk8kg4jis0Vem7j3w7Nk6\n9qx0/AWKUgV4nkfHjh3h6OiIkJAQrF69Gk2bfgCi0yAC7OzuoGFDe9Rp3hwmd+8iz4Det4uLCyws\nLCp0HwHGnwu5XI5evXqhXr16eF1eiscIeJ5HSEh/eHrWhVT6fiq7hnDvHtB7oAx0xwP7jcgOjQ8P\nR3MlIccQ5HI5HB0dq48l9d++/dUGg+eBQYOYrJKR1Z2R43k4OjrCfoI9c0td240pkgNYdn8Z+rj1\ngfn35my/K2FP7z06lckeP2a/zIULhs+R/Wc28wfv1vAHv32L17t2obZIhI+JwFtbY/fyviBXwrn5\n7N89577W6qfBTw0w9w/DgT114ZAWZcWWMjIuw9vbFqGhQ5GU5Irs7PtMnmPZMpTWIUj+JMTdH13p\n+6VQlCA1dT9iYuYiJKQfPD3ramXthoR8hBcvFLhwgUlodegANZGrd2+gZUtr9OxZo9Ln+0egpISx\nMIhQOLY7VFUbi+6dAscRUs5UfH8DAhzx5MnHAICYOTGQmElQ8qqkgqOAG0pOP/eeEuPlIZPlw+Nh\nPXB7nJD/NB937twBUZmcfW4u0KNHKIiA/v3vonnzFrCyssJZb28Qx+GUgURYf39/EBEOHTqk9/PK\nYteuXSAiXLx4scrHFhSEguOEBtWT/wrMjYmBhbu7TrBbEztTUkAch1flKfnloLr3+KsMBv1FFff+\nju2vNhgAo7OZmekWV6ks9u/fD6pNasNArgSzTWboc6wPXPa74PtO38NitQVGjR+F/GDtuIhCwRit\nw4YZP0fokFB41vGENKfsAZo9ezbEYjEiL1wApk/HR7MFcFzARtePXJvCbpcdSuVlLokhZ4fAfre9\n1j4dODmxR8XdiNR5XBwjv8+cichN5vC4J4ZcXjkiPMsIJnh61kVISD/ExMxFSspuZGXdxdWryWjR\nQqE2EDVqsPuyZUtZ7YFhwzrD1JQqVUr3H4GUFCb7QgQsX46XKQfYqqKQBXz9r1gj1E2kn86nhCpI\nnpKyE8XJxZCIJYj7WleiXB8WKQsmlVRDIatngUw2P+7KSQwcOBB2dnYoLS1FSgrQvn0pRCIpdu1i\n8Sie51FUVASe59HU1xfDDVBGVSuVHj16vPN1BURFwdzCAmPGjHnnOFxs7FfgOBEKCsJY0utfwDBT\nIV8mg5W7O2ZVoK/l9+YNiONwRc+zUVrKJqMrVwJOTvxfbjA+Um4/E9GvSnrtaCK6QERuVT1RdW7V\nYTAAlmhNxAhDVUVeXh4sLS3R79t+WMDtAP1xCOdevQDP84iKisLmqZvxweQPYLPJBjKF7lJ7zRoW\n6DJW/KUgtACcoCyI6e3tDSJSSwBkFWZBtEGENZsHAsuX437sHZAr4VhwWbLR3fi7IFfCiRADKmgA\nEBAApUPZcJsxY9honp6OvB+nshlxVMWaCVJpNjw8aiAiYpKez1hgs107loUbFKSbiTt1KtC791cg\nIty+XbYk+8e6pCIjgbp12b387TcAQETEp/DxsVcPZPEBsyG5T5AtmGWwG1XezNu30Tgz5gwkJhKd\n2JkhtPf3xxBjSnrvAbm0FNzpD3DMrTGICDt27MCTJyz9x9q6GDt3DkJxsa5K8cqEBIglEmQZmF27\nubmBiNQ5Boag+VyUKhS4/vo1xoaFQdC3L8jKCmMfP0ZYBbVYDEEqzYKnpw2ehDiDHz2KvTPNmgHz\n5jElw/dYsR19+RLEcXqD3ZooVShg7u6OxUohwpQU5lofPRqwtmaXJBYDH32EaothBFVm3//lVl0G\no6SEafs1bVr5zExNfPHFF7CyskJEZCQarF+PeiNHonHjxuqAE7VjK4+HiQ91jo2JgU6unT48nf4U\nF0wv4M75O3ByckK9evXUxYfOhJ4BuRICUlmQked5dDvcDS33toRcIVfv63KoC9rsa6PepxeqWIae\nJCa1GNe2bazPmBgEHCUE3LKtcLb27NlacByxWVk5XLnCur150/DxubnAwIG3IRYTFi4sk+7+xxqM\nRYsYlVlZ15rnFfDyqo+oqBnqJjk5j1hcpy/p0vmUePp0JHx9m6M4tRhuYjfEzKtcQaJXyvyL7Qak\n5f8K+E7fiYEDCdbW5oiMfIMaNQB7ex5nzjgbrAYYkp8P4jgcMeAjzszMhImJCb6toBj248ePEZyf\nj2/i4lDX0xPEcah77hyICB926wbre/dAHIfRYWEVDs76oCpvnOFMrJzf2LHM+BOxGWCvXkwz/YVu\nsTZjGBsWhiY+umWk9WFASAh6BAXhxQumoquyWwsWMJHE/HygoCCs2gxGNBE11/i7GRFFV/VE1blV\nl8EAmMYMEVvGVRUq36p6q1ULgydMwJEjRxAfH4869etAvF6M+Tfn6z2+d2/dSqwXL17E7Nmz4ezs\njCZNmkAkEqn7FwqFuKZRAGDirxPReFdjKDTqif8W9RvIlXAp/JJ6368Rv4JcCVcijVBT79wpe/I0\nXRUyGbvIZs0YvVeJl0taMX56rqfBLqXSHHh41FQrmpbHwIFAkyYVs9U4Lg1OTgR7ewfjDf/bwfPs\nPo4cqd5VUBCmlKA4qd6nUJTCw90aMavN2FSxfF6QvBDu7uaIi1uE1F9SDZYf1oezaWkgjkNwBfTx\n98GDyQ8gFBKmTLHAN9+UQCQC/PzuarHvyoPnebT288NAI2UDJk+eDBsbG3ViX3n8mZ0Nx4AAEMfB\nVCLBpxERuJ2VhVnjx8OCCK8HDkROo0bYOGsWbO7fB3EcBj55goc5OZV2U/HcQwQcJfj8YQm5TLlS\nkUqZKsP69Ux9UChk6eiV7FOqUKCGUjW4Mvg+MREijsPqDXIIBMxBUP5UiYmrqs1gDCOiFGIChO5E\nlExEQ6t6ourcqtNgAIy1JBaz+rtVAc/z2LZtG3bt2gWvoCBYSyT4XEP8b+rUqTD73AwNfmqgd3av\nSplQsRtzc3NhYmICGxsbfPjhh/j888+xdu1abB2+FbtpNzzPlj1QxbJiWG2xwryb87T6VPAKtN3f\nFk6/OKlfArlCjlZ7W6Hr4a6GXwyeZ1ViiBiNTIVDh9g+zeIBAORnj8LjJiGSGwhDePZsPVtd5IcC\n0dFMNDE6GkhIQNyDZDSmVOz5PqPCLCye5zFjhhmICOfOZRlt+1+NiAh2LzWCt6pSucXFyVpNw8PH\nwedPG/B67n1W1i1wHCEp7Rr2uOyBywgXFEn1VOnRg1nR0bAxki38V+CLAV9AREIcPVoPFmbFONHn\nCMIlA+Dj84HRXIZ1z55ByHFIM2AQ7t27ByLCr7/+qrW/WC7H4vh4EMehjZ8ffklNVZceePnyJUyE\nQiwUClnRslevgGnTUGBujl0uLmj06BGI4/BTZVZcr14BDRsid6QDOI7w7Nk6/e2OH2e/cyXyPADA\nIzcXxHG4WknmFlP65VB3UA6GD9f9nOd5+Po2rz6WFBGZEVEn5WZW1ZNU91bdBiMzk7mV+/TRnlxX\nFd/GxcFEIlEzGM6ePQtqz9xSXBKn0z47m0mVLF7M/j6nXDr7+PhotZPmSvHI2hM/USh+3PQIPM/j\nThyLV9yJ080APB16Wqd40tHgoyBXwv2E+4a/gMqCNWzIyoTl5THhwgEDdKcwhYWIW2oKyUMhSkt1\nayCoVhcRAWMYs0AV1da39elj+JqUOH68A4gINWteRnr6P9QltXUr+74atMmwsDHw9W2h0/TlyyMs\nRjG4FfOZFhcz6e30p1h2vTc67xFCvFHMCBczK4hRKcHzPOx9fDApIuIv/VqayMnJgZW5FQbTYHw5\n9SqGElu5vhxFSE42QO9WIuLtWxDHYZ8Bd45cLoeDgwOGDBmi3hdWUKBeVXwdF4d75dQQVixdCiER\nEjVWdQAYwaNDB5SYmKDP+fPo6FVBJrdMxlZ7lpZARAQiI/8Dd3cLyGR6VmpSKSu60bVrpVYZa5Qr\nBmPsKE3kKIUIaVoSfv9d9/M3bwLBce+Wh1HZmt7diKiD0mB8JhAIZlTyuH8F6tUj2rKFyNeXKCDg\n3fv52s6O5AD98uoVERENHTqUKIHIhEzoSuQVnfY2NkSjRxOdP08kkxFdv36d6repT+07a5c2LxWb\n0AVRE+pOuWSxLozche50aNkhspBakGkfU/Ju6E2hg0JVxpWmdJxCTWo1oS2eW9T7pjtNJ7sadrTV\na6vhLzB9OpGVFVFGBpGbG9HmzUTZ2ez/AoF2W0tLshNPJIh4Snu2T6er1NSfSZSeT23nJRBducKK\nH1+5QnTxIpUePUMLLU7Q0R5HiCZOJPLzI8rPN3pve/bsRlZWAnr79gF9+SWzNP84/PEHBbZpQzvO\nnye5XE6AgvLy3KlOnYE6TW1shhMRUfaqjwnJybT6p2Hk4OZAnQ51ol1P/agY1rS4w2Lac3IPNRY1\npuNPjld4+vjiYkotLaVPatf+y7+aCocOHaLCkkIaTdPo12tjaWW9TUREZHuPyFY6xOixHaysqKOV\nFf2aman3c5FIRLNnz6YHDx5QUnIyub14Qd2Dg+m1VEp3HB1pX6tWZCYSqdvn5+fToV9+oUlE1HzJ\nEu3OBgwgevKEzLZupcl37lCETEZJW7YQFRXpv7h164jc3YkOHSLq0IEaN15IPF9M2dl/6LY1MWHt\nQ0KIbt40+p2JiO7n5lKvmjWptolJhW2JiOqYmJB1phWZdc+nkSN1P8/MvEwCgbhSfemgIotCQBhJ\nogAAIABJREFURGeJyIeIDhLL8t5HRHurapmqc6NqXmEAbLYvEjH20vtgVFgY6nt5oVjpmO/Vqxfq\nzK8D2522et1SN25A6fEpgnkDc4jXi9HvhHYxoxUrACEp8E3LV5glTkbUygQ0/KEhhq4ZirhFcQgd\nEgqOOC0V3gMBB0CuBEmSRL1vt89ukCvB94WRxJ/Fi5nesoUF89N98YXhtiEhCP2J4HO/DhQaTDCp\nNBchh6wgrW/OqBvlotpHj7Lv7OkJ4P599sdDXWKAJp4/346+fQl16zYp79X5R+B1ZCS+1Ih3Xbt2\nTT0TTE/XnxcQEOCEJ0+ccWlWd5ArYcTxgTjgswFX7hFevjyCtLNMEWDTlU0gV0J0pnFK5gFl/Yv4\naqInl5SUwNbWFkOGDIFLzWTUpUwoxCJkfERQiAVqoUtj2JSUBOI4pOipUQ0ASUlJEAgEaDR6NOjx\nY4wOC0NGqX7K+E8//QQiQqCdnVHXQbzynD9PmMDkci5f1l4ZqKpUquqvgpEVfHwcDAbxIZOx3KYu\nXYyuMjJLSyHgOGxISjLYpjwSEwFaEgOzBx6Ql+ub53n4+DTB06fDqzXoLahqx3/n9ncYDIB5XsqV\nlKgyHmRngzgOJ5V82Q0bNoA6MreUR7KHTnuplHl9+va9ARpdltNx6skpAMztrRq3vbzYL7rhaADI\nlXA6lCVEFYSz+gdpp8sSn4qkRWj4U0MMOVu2fC8oLYDNdhuMuahbY0ANld4yETMcSjaPIbye0Rwc\nR3j9uiwY//rnSZCbEhRNGusUe+J59g6pg/25uexcW7YYPU9m5g0sWsQG2379EmBhATyruMbP/zlk\nMhn27duH2paWEBNh+fTpcHBwwKBBg/D8+XZwHOl16QFAQsJK3HskgsMOW3SeL4C8ZXMke8wHxxFK\nSlIR4xIDj1oeSMtLg3ijGN/9+Z3Ra5kQHo4PKsnEeRccP34cRISbNx+hjqkMbqY/AkSIudoPpV9M\nYHk8GrkLb6PfIn5ZvFbtDZVekj4V3VKFAntevID5zJkgIkzdts3gdyktLUXjBg0wkIi5AitAW39/\nDOI4pklCxCogRUSwh6x2bfbQljNiCQnLIZGYQCo1oM576hQ0VRT04WJ6epVFIFetAgRDGXnhaTmK\n8Js3/moSRXUZjCtE1KiqHf+d299lMH76id0xAzVKKgWe59HB3x+dAwPB8zwCAwNBpgSTDSb45o7+\nLNFFiwBBg7Gg9YSvb32NPsf6oP6O+sgqzMaAAUx3MDOTTZIaNuTQYu5aiDaIkFXIAsC8godHTQ/E\nztce3Ld7bQe5EgJfBqr3uXKuIFdCeIYRaY9hw6CmCY4ebXR2pji4Dz6XCKEevQCFAorvlwNEKOhW\nVy1Rogk/P9b1Qc1S423asDwPIygsjMXp08xgbN16CCYmHObMMXpIleDn5we5HrqWglcgOTcZ6QXp\nKJQWVmmw9fDwgJOTE4gIgxo0QJRSs2vz5s0gIvz+ez/4+3cweHxurjtmnWQTCPcbe4EmTRCylxB4\noyFQWgr/dv54OuIpOI7DuEvj0OCnBtpS9hqQ8zzqeHriiwoSw94VCoUC7dq1Q+fOnbFnDw8iHlnU\nAnzPXqxBcjIzGF+VaYKFDgpVS/1r3teugYHoERSk/pvneVx//Rot/fxAHIdBwcHoryxH4OenXe9d\nFdtS6SndEwrVNV+MYYWyBGpeSQlLbKhTh7kc7O1ZdUo9Mir5+cHKDP0j+juVyVhZgk6dDL5Ds6Kj\nUcfTU2elYAilpUwLb/CMIhDH4WA5GZH4+GVKI5ZbbQaDI6JcIrpP/x9leutDdDS7Y++qMaXCYWUS\njntuLhQKBRo0aAD75fY6FFgV/P1loCkmEK0xQWZhJkLTQiHcIMTA3fNBBBzW0DybMoUDLXDEh0c+\n0uojdEgoApwCtPa9KXmD2ttqo8+xPiiUMjdEdlE2rLZYYdo1Ixr/gYHAtGmsAAERsM4AGwQAcnOR\nPEsMj5sE2RimoPZqBCE/y09v8xkzmJdKi9U5YwYLtBt5aRQKGThOjEaNamDixIkYN46DWPx+xl2F\nhw8fgohw/vx5nc9URle1CTcIUXNrTdjtskPb/W3x2ZXPIEmSaA14crkcs2fPBhHBwcEBVy9eBG9l\nxRK8AKSlpcHExASTJ4uNSk0k5yTCbCNh2HFWQEqanQTukQDPZhNKO/ZV1+zmOA5/xPwBciVcj9Y/\nmw1UZgifT9e/mnlf3Lp1C0SEU6cuwN4e+KKJJ0CE4nVltWUwdy5jebx4gTzvPHDEIcApABxxSP2l\nbODb8fw5iOOQWFSE4Px8fBQSAuI4tPP3x52sLPA8j+zsbDRr1gx2dnbI0Mh65jgOCoUC7du1g5NI\nBH7cuEpdv6eSqfSrqq/MTPZ7mZszv7Ee8DwPP7/WankWvThzhr1DyiTN8sc39vbG5CqQEC5dYt3d\nvcejkbc3pmqwMsu7yarLYHykb6vqiapz+7sMBs8DLVtWLNlREQrlcth4eqqrmc2YMQNWva1ArgTv\nFN0Slrt+Y7GFeuM+V+9b8Pti0A8CtB/srzU5ue39DORKmLhzl1YfSa5J4IScTg3nyxGXIXAVYPi5\n4Wp5kKX3lkK0QYRnORX4dHiecY4NPPAqSMd9giJbAi8SIPEbC4Q91e/XzcpiciwLFpT74MCBSi3t\n/P3bY9y4D1CnTh0kJ8thalopt3iFGDt2LIgILho+aoC90C33tkSXQ12w338/tnluw5pHa7DoziJ8\n8fsXmPjrRNTeVhvkSuh4sCMOBhxEfkk+7t69CyJWOa6wsLCsCPWtMtbahAmfwMqKkJRkWNdoytUp\nMNsoxNWHDXD27Fn4+yuLTN3agde1RoAjDrlf/QLI5ZApZGi0sxFGXdB/77cpB+F0A/7+94FCoUCf\nPn3g4OCAw4dlIAKS+n0BOZkj/ZCGXMmzZ8y/+s03CB0aCq/6XpDly/B02FNITCTqejLJxcUgjkN7\nf38IOA71vLxwMDUVMtWL8OYNwPMICQmBubk5nJ2dIdOQCLh58yajYBMBd+9W6jvIeR51PT0xrbwS\nbAVJQs+e/QCOExiuyqdaZTg56awywgsKQByHY8bkHsrB2bksVWpSRASaaDAq8/J8wHGEtDSmTl0t\nBuOfsP1dBgNgKuKmpsA7qgeosTIhAUJl8O7SpUsgM4LpRlMsvrtYqx3P82i4piFoKYHEmVDVj5n7\n9RvQskZo69ZVK1ju5rsH5EroPkS75kH2/WyD1c5UlNpPr3wKuUKO1DepMNlogq9uVaLuQnExy161\nstKJR0ChAHbsAEQilNYiBO9nYoL5+UF6u1K5/HTyXYKC2Afl+PXlER4+ERs32oKIEBAQgPnz1RPW\nd0ZSUhKEQiGICB06aLuHvFO8K5RVKZQW4ljwMXQ51AXkSqjxYw20+KYFarWsicJCpVTEwoWMRFBU\nlivx669fgIhw+PDPevv1eu4FciUs/mM0tm1jrriJE1vAy6s+eF6O+AVhkAgfQEEmjO5ZUIBVD1ZB\nuEGIl/m6g9eg0FB0DAjQPVEVkJrKfqLyNueXX34BEeHo0ZNo2RLo26kAvLU10kTDEb+0nHruF1+A\nNzWDN13B8+0s90GaLYVvU1/42Puoy7sOCAmBqUSCFQkJ2iq2ISGM2jp5MiCV4vTp0yAiLF++XN2k\nf//++MDcHFIHh4qzQhUK4No1gOMwIzISNp6eZYapEnj7NhocR3jxYo/hRqoCaOXyaVRCginFxfD3\nB/bt05XG0YTKA6IUXICb8vgXythKfPxiSCSmTCgUf7HBICIv5b8FRJSvsRUQUX5VT1Sd299pMFRK\nskbiVJVCjDJ4dzA1FTk5ORAKhWj9Q2vY77bXcktdCr/EZqjTu0AoZKoCQUEs3jx0KfvsQECZj6zz\nys6o79oeRNraZ7I8GTgBh6SNSXqvZ6f3TpArYc6NOeB5HnNuzIHZJjOkFVTs38XLl4CtLeOWZysN\nUkZGWaxj4kTkDbIDx5FB1ohCwUgj/fpp7w9+FYz7UbfY0l9fKUQNJCauwbVrbHCfM2cOkpPVE9Z3\nxsqVKyEUCjFv3jwQEbKzywyuyx8usNxiifySirOieZ6H7wtfTLowCbSWua/6HawNr6QHjHkzdqxW\n++DgAWjRwhxdu+omUyp4Bbod7ga7XXZ4mRmBxo2ZwWjUSKiWEAnqGYSQ/iHAsWPgiAA3N8RlxYFc\nCVs9tYO8xXK5lv7Qu6CgAGjfHmoxgFOn2OCWkpKCGjVqYPDgwbhwgVXFC/zqBECE6DbHEDqonGZV\nYiJ4gQip5pMhKygbHfOD8+Fu7o4nA59AIVMgWyrVTeDLzWXPYK1a7EImTACkUnz1FdMau3z5MhMF\nJYIbEbBhg/EvFR/PmC5Kkkd+ixZYumABvBMqLkAFQP0eBwZ2RlBAT7y+9hrRX0bD284bMS4aWdty\nOYvTdeyotcoYHBqKFp7+WmlKI0YYnqwuXszCQCqvmcrNeCkjAzyvgLe3HcLCyp6z/60w/gZIpex5\nNMYmrQx4nkdzX1+MUk6n+/Xrh6Zjm2rRWkvlpbDfYQ9aQDh56iSGDmVSGT17Mpd+Tg6PQWcGodbW\nWkgvSEdOUQ6Es4SYf2U1iHR1qAI6BuDpMMNF4tc+WgtyJSy/vxyxmbEQbRDh69tfG2yvBR8f9rQO\nGcKosLa2zL/0yy8Az4PfsR2pYwlF4frpsSqvjKak+9vSt7DfbY8aP9aAok9voG9fo5eQnn4OHEdw\ndGyDLsoiyF9+yS6jCqt6NYqKilC3bl2MHz9eXdLyltJtVCwrRq2ttVispwqB7p07d4KsCBN+NkHN\nzcxwDJpF8DiwQt1GLi+ERGKKDRsGgYjg7++v1cfJJyeZZP3Tc9i0aROICP37myhXVvsgfyuHRCxB\n4vcsEMs5OrJRXC7HgJMD0GpvKy0j9CgnB8RxuJmZWfWbBPb1J09mHIjt25nqBRHQpg2PTp22wtLS\nGomJSXB0ZNpsfN++QJs2iP4iCl71vbSu5U3AG7yiYVCIdX+0VydfgSMOiav01OngeWZ0xWLA27us\nrum4cSgtKECfPn1gZWmJvq1aoY6ZGQoEAsNLT7mcxecsLNjLfuwYcPo0ZH36AESQmZgw1Ut3d4O/\n/ZJ7S2C73RZ/7PoDfuu+ZVL9jc7Do6YHgnoGMdbiGY3J2Pnz7HovXwYApLyWQ/RQAuE38bC0BH74\nAdi7t0xVpHycvqiIkbU+K5NTg1QpRLgkPl5dTCs9vSwO9z+D8Tfhs8/YgP2+6s8LY2Nh4e6OYrkc\nW7ZsAZkTTDaaYNn9ZQCAvX57WSC1tRDZ2dnqZ4qoTJ0jNisWpptMMf3adJx7ek5tcDQLx6sQ4xID\nz9qeZaVdy4HneXx9+2uQK2GLxxYsuLUAog2iCvn7aqgSKIjYyKApR52ezgzKvHl6Dx0zhhX205w0\nrnm0Rh1MfjZrHFtlGMl2zc8PAscRFiwYA1NTUxQWFiIhgZFZliyp3FfQhIpJ8+jRIxQWFkIsFmP1\n6tUAyvS3/vxuAhtU1qxhQRgj4HkerVs3QYcOhOfPtyHp5WXMPy2AzUb2HQecHIAHiQ+QlfUnk/ZI\n+g3W1tZa1eTyS/Jhu9MWfY71QWJiIszNzTFiRDucPMlWGYcO/YychzngiEPWXeX1/PYb+02uXVNn\n+WuW5VVpD+Ub83cYwY4drPsdO1Tfk63A7e1zQQQ0apSJlStZm+tblX6Tn37Ci59fgCNOq0ZH2Kgw\nBNa6CN7AjxYzLwYccXh9rRzDbvt21q+bW9m+vXvZvjFj8Co4GH+amgJEyBMIWHY8x+n6eKKjmbIA\nETBqlFbWPQDMvXoVZydNKlvFdOyoUzTnZuxNkCvBdI0pTNeYYuvYVeA4QjS3FgqpAgqZAiEDQuBu\n5Y7CWGXOi1wOtG0LRfsO2L5VAcuPGP1+2PosLbt56xbzuDVtyi5VBRVDl+PA2IfHjgEjR+LD/fvR\n9949xMV9A4nETCvz/H8G42+CqiJfuYlflaHSfLmfnY0nT56AiNBpeyc0cWuCvOI81NtRDxbzLTDw\nE6bHVFjInlNnZ+2JjWpgbbe/HWx32kLBK+Dmxq5RU69MNUN7G2lYiE7BKzD92nS166Lm1poYfaFy\nxZASshOw4RMTHOgjRuor3fyMhG8+h9RUpJMg8fw5mzkpx2J1X6abTDH58mTU+LEGDn83kH2h4GCD\n55fJCsBxhLNnZ4GorDDPzJlsslgVAhDP8+jWrRvatWunngH36NEDAwYMAACMODccduusIBcQm/IJ\nBIzetWqVXrowAHh5eYGIsHq1NWRKYbrsaa1x/y5hya+2aLzTFuRKcNxni9mnhOCe3ce8r+bBzMxM\nXe961YNVagXiMWPGwMrKCpGR1/H4MaFePVP85z//wbMfnmkTHORyNsL0749CaSFqbq2JGdfL1G97\nBgXhQyP31RgePGC/3eTJ2s9kRkYGbGzqoVWrdWjdmrmimjYF5EuXs1VARgZyJbksrnaPufnyg/IZ\ns2tzMmPG6fnRFCUKBPUIgkcNj7LBViLRfxEAsH8/e27MzaEwMcEVW1uUELHgFhFLcpozh4lrbt/O\nlqN16rC4gp7Vw74XL0Ach7jMTKYJJRKxzFkl0gvSUW9LPTSf3xyPpj1Cz/09IXAVYMnlploU6eIX\nxfC08URgl0B11cy03RcAInxJR9Hsp3iYchIU6omxBAayyVWdOoCHMnVrTJcUbGqwF7yzM7sXyhu+\n5LvvYHX/Dry8GyE8fLxWP/8zGH8TsrKgjie8DwqVvuNv4+LA8zwaNWqEHnN7sKzd8yPY7LoxYf/+\n/epj4uKYq1arH2khmu5h7qyRW5gmzsuXbAz74QeNdrGF4IjDq2PG/TMyhQxjL44FuRLGXxxvUIJd\nEwpegY9OfoSaW2vCbJMZpv42Vf0Zz/PY4rGF9TdFCMWsmVrHLlgAHQrs6AujYf2jNV6GeuKz/c7o\ntroudBM0dOHj44CIiM/RqlUrNGnSBMXFxYiNZb/Xd8bz1rTg5+cHIsKBAwcgk+UhIuIzLFw4A+bm\n5niemQTRDwKs+oSQMXo3fJv5IuuXYGDKFHbTLS2B5ct1BrupU0fA0pIQFbWR7UhLA4iQs3c23N0t\n4eHTGnt9fkSb3ZYQKFdWFpssQNMII7aMwOWo6zDdZIqZ12eqmT7bt28Hz8sRHPwhJk78EA0aNEDI\nxyEI7MJya4KDgXatHyB50U52/4KCMO/mPFhstkBecR5ypVIIOQ7r3yHLMTmZaax16KDrV//ss89g\namqKyMhIyGSM7hnkK2Uj3Xg2cElzpOCIUwe3w8aGwbO2J2R5Mqh/NI1gtQrFz4vhVc8LXvW9kLol\nEooGjYHWrRk7ShMKBTMCqgG0Xz9w3bqx4hu5uUw/f8qUMvlxIjysOQ5DO6Whb1+mljx8OAuFqIQG\nVAytnaoA4fjx7CYotbxGnhkJ03WmONflHGQFMhRJizDx14kgV8K4I4TcN2Vqu5k3MsERh/jF8cjO\nBtq0UsBD/DHk5pZo7+mJQUZqkjx7xsIe5iZyPHWcqr5+dOjAaO5PngA8j4vnz8OJYwKWGRmXtPr4\nn8H4G9G/P9C58/v3M+zpU7RSJhd9+eWXqNGghlo0zmkDS+pKNVLDV4VbsbcgcBVg5/md6n0ff8wY\ne6qJEs/z8KzriegvKnYxFcuKMfL8SJArodbWWnA66GS0XsZ+//0gV8LxkOPqWIjXcy8USYsw5eoU\nkCuh6+GuIFfC2oGkXvrExzNjoUmlVQknbn+0EWjSBBc7EugHQmntmmy5YAShQR8j6KYddjo4gIiw\nc9MmAMDnnzMiV2Xd9NOmTUONGjWQn5+PlJSd4DjCjh0dGR32y/YgV0LU9y548vETcMSBIw4JyxOg\neBoFTJ/OBikLCyZpLZMhLy8P5uYijBljrl5d4Ngx9gqGhiI31wMeHtbw9W0BjhMhJHo5rkVdwzd3\nvoHlcsuyXI9NFpjo+yfsmzZFu3btUKpBSTpx4gSICCfMT+DZbHfwbnsQWqMfHikHE54IEIkgq1UT\nr6wJ+Y3qImXCBIgePoR7+VlIBSgqYtp5tWpBzdxT4ffffwcRYZPy3qtx7RrK04d97LwQWXc38rv/\nBxxxSBpzlS3d375lP5qlpe4MCUDB0wKEDAgGRxz8BOeQsStImxyQmclGeyK28lDGNDginZnerp3Z\nGD6iCYZ/Vgejxhdg+HBmLPr2Bbp3Bxo15GFpWaYa7RQQgI9Ufzx8yM5x+jQOBR4CuRIW9lqIXEnZ\nNSt4BZbe/QrkShh4tCXC08PxZ8KfePTsEbhZ7Nn5vKcXxB8E4srZx0hp1Yop5FZgxLOzgXN2KwAi\n7BEtRa6frvx5YmYmvuXG4tFDk7LnTon/SoNBTB49hojiiGilgTZ7iSieiEKJqLNynz0RPSaiSCIK\nJ6JFRs5h9MZWB1R+2/etwrhXucSNLyzE1atXQUTotbcXTDaaoGO/jujVq1el+8os1B4NVSEFjaRY\nhI0Kg3+7yvnSpHIpZl6fqR6sjgYf1dsuMScRllssMezcMPA8rw5WdzjQAd0Pd4fAVYCtnlvB8zy+\nvDQV5Eq4MJcp0E6ZwsYElZ+2RFaCVntbofW+1ij9ah4gEODNim9huo4QUZ/YCKWviE5mJrB2LeKW\nmsLjNoFv3w7DiFCHCDmLFyPWMwMCAfD99xV/7/T0dJiamuKbb74Bzyvg69sc7u5WuHpVyUaaT+jx\nQ2NIM0vBiTjEL41H7IJYcMQhqGcQihKLmCWcqpz5DRwIty0LQUS4cUODRDBmDKvFqxzo8vJ84OFR\nExxHyMnh1M0uXboEsiLQlqno9vAExLOYy63nkSPgNGo1pHp5YSkRnlFD9YzzqUV7XB7yNXbUXYcQ\ncXfwQiH42bNxuV8dPOxWByDCptmzUVqFgBzPM7tNpFvcKjc3F40bN4aTkxOk5eNNI0YwiXyNuEGY\n0y340wmE1/oZHnQTUlJW/BEIWBY1EQtm37jBXjYNo8B/twJZ1Bv+dn+CIw7BvYOR65HLNHLs7Jjb\n6cCBsmOOHWPTcg2p8itXeNDE/4B+EIBcCbt9dmtdclFSETztfLDdIgJNG8uRmlqmHpstlbK+27RB\nUVcnWGy0QPdp3RHzrf66FWuut4XQlcpUhF0JJmtMcMT2CH63+B31ltYDuRJWn9sH4jiEGUuIBdSB\nC/cOC9RU2vJQKGS4/rg2Tl1sU8ZgVOK/zmAQkZCIEoioCRGZKA1C23JthhPRbeX/exGRn/L/thrG\nw5qIYssfq9GH8RtbDYiKQmU8JBUiXkmv3fviBfLy8iAWizF/9Xxc8rsEIsI2Q09CJZCTw+LMmmzU\n5C3J4IiDNLtyUsk8z2P5/eUgV4L5ZnO13IgKCl4B51POqLm1JlLyyqznZvfN6jrmN2LKMmFL5aXo\nv94B5msIv548DyLtQXyb5zaQK+HuVWXBbqW2+/CTg7DzYzO2z9KS1c8tLGSWZtkydWmx1B86K+tH\nvMDTS5cgIMJ3RICFBW63WoS2Vila701eHpvwLl/O0knc3KCW5oiOjkZW1m2W7PTyFPyv10T9tuxF\n3++/H2mnmLjfm0DmCnl99TU8annAo6YHMi4ruY0nTgDm5ujwgQAtmovKZnlFRWwFsnCh1v3Mzw9G\nYuJqKBRlv8/b4mKIbGxg3b8/YuLiYGZmBsfRo1HfywvEcejv4YG0/v3VRiKarLB7+jy0OnOGyVxz\nHCw4dzRYEoiUevXxZtFauPm6gVwJvw3qB7lQyFhulYQqj1LT3QkAPik+6LW4F4RCIYKCyuXapKay\nVVc59c7EJhvB0SNwxOHZukQgIYFFzDdsACZOZA+wyt1CxHRwBg4sSxidPx+8nMer46/g3dgbXnQN\nMpEJpLYfQCoxPjHy9ARE/XaBXAkbHv+IgacHwnanrbp2iDRLCr82fnC3cgcn4HBAGIx+TlJw6Yyu\nek7pcpS7McWDj2Za4abTTS3tK028enUCW68SBK6EOtvq4GjwUcza+BAODvfxp8ljPOz5EHV/rItm\n90+i8Z07bEVoqD60tzcziAMHGiWC5OQ8BscRpl2az5hfGvhvNBi9ieiuxt+ryq8yiOgQEX2m8Xc0\nETXU09fvRPSJgfMYvGHVBZ5neQMjRrx/X638/DBMyShydnaGk5MT9uzZAyJCbAXifuVRvg7E6NFs\nsqWaQOZwSgbNnaoVGlKxp5ruaYo3JWW+YpXqrWad8AthF2C+2Rxmm8xQe1tt5BRp1zJ+nRqHJksE\nqPudOWrZp6o9DqlvUmG1xQpjzo5kNNAWLdS1cQ8HHcYn05WDRt++7F8VdVcoZO6LiAjk5HDgOMKN\nG4xTPHPmTJiZmiJ50iTwYjGkJMbD1guw6tsidO9e5t42NWX1wy0sZGjUyA6DBw8GADx9OgLeXrZQ\nTJ2MrJ6ED+YSaB0h820mwseFw9vOW8sVUpRUhODezFUS4xIDeZEcnuc2gIjg2lVQNuO9dYud+N69\nCu/9L6mpoOnTIRAI0Lt3b1hbWyM1NRVFcjkOpabi9iefQC4U4vsvv8TYugNhIbBE18thoEkp2HE/\nF4dv38aMqCiIOA7iPx9ixvI1uBcRD5ONJqixdyxyHRzY/a6EwN3jx8yFOGqUNkvQJ8UH5hvNQa6E\n2Stn6x64eTP7vpqaS6mpyCBncMTBo4aH/knM+vVstfHHH2x25uLCeOXm5qwkpQatTl4ox4OhQwEi\nOH/eAKfqn0Jg50DEfRuH19deozSzVP1+REUB1o6PQetFGHVmAnieB5fEgVwJ+/z3QV4kR/CHwZCY\nSpDrnouMKxl4bCLBafLD9MFFaOjlhc+Ukh0bbyxDgQkhpHYX5PkYLusqlebgwSMBXM7Vhv1ue5ht\nsAK1uYHp04FXJ9nk48dPt0L44CZmhYcDjo5MGOrVK5SUpCE3V8lse/6cxYJatNBZNZRHbOx8PJRY\nwPzRbeQ7Omqt0P4bDcZEIjqi8fc0KieNTkQ3iehDjb8fElHXcm2aEqv0Z23gPEZvWnWmlmH5AAAg\nAElEQVRh8WI2Xr2tXPVLg/g2Lg5mEsaI2LFjB4gI7dq1Q/v27avcV3mDcfEiQGZyXOXYiyV/Kwcn\n4vBsbdWDnD2P9mQsnoOOSC9IR2xmLCw2W6Db4W44FHgIKx+sxJiLY9QU0UfPHkG4QYhFdxbp9HXH\nZSGsVxOarW2n1rGacnUKzDaZIfHbGWyQUFFAwNgntVYReIEA2LSJceCHDmUMF42Es5KSNHAc4fJl\nlq2XkpICMzMzTJ8+HUhOxt1mCwAiBAh6YEKvVKxfzwbBoiJGUxQIripdRzdQVJQAjhPg2VrmGpFu\n+xFWP4hAnxIin/jB3cIdsQt1DbpCqkDiqkRwxCFiUgSmTHGAqSnh9fCP2Ss3bRqLc1hba/OI9SBf\nJkMDLy/0vHNHnXG+a5eG7IsyPT7O1RVeObnYYL0RRIQaNXygqiOkeiaSiorw6RUOZvfvQ/DoMWod\nGgTaZAHu8hFmOSuID4WFATVrsriqZljhSdoTWGywAH1LoPWE5XfLBar9/VmSwCefaO/fuRNF1Jjl\nVqzRk1sBlKUva9JlAcb8KudGOxt6BlH1CGEta6L+lvqo4VoD+ybug7u5uzrOdKjFIcRfzIZd++cQ\nrKyHlm7t1ImXPM+j34l+sN9lj+AJweAEXNlKEUCuRy4eWHjiKnlj+MYw1PLwAJfkDqGrELebOLDc\nESMD+IPEB9h0hfBAUhu/P3oBgUsP0A8CbHX/CQqFApGfR+Kx8DHaHuSwO+EpEBkJRQ1zPF/TCh4e\nNcBxhOzU35lYYc2azOoZgVxeDC+v+ngQMg7EcZB06gQ8eqT+/F0MxjtW0fj7IBAIrInoKhF9C+Ct\noXazZs2ipk2bEhFR7dq1qXPnzuTs7ExERBKJhIjoL/971Chn2rOHyM1NQv36vXt/dtHRVPrsGUk6\ndqQRI0bQihUrKDo6mtauXVvl/pydndV/9xswgDJ7pRN9f40+DVJQ2ocLqIGVKcU2j6WEOwk0Z9Oc\nKvV/aeIlar2/NUUGRFKT4CZU6lBKRETBPsEU7BNMJi1MqGntpjTJYhK5OLjQwGYDaW7XubT/8n7q\nXNKZZo+fTUREHCehNZLhdEh4hqZ/Fk2jfhxFY9qMoYuxF2ldkxmUsu4MpUyYQM79+2udv2OrvpTU\nMIhSbt8m6tePnO/dK/s8NZWcnZ3J1LQhhYdbUe3az4mIyMHBgcaPH09nz56lpUuXUu+Qg3Tqu8bU\n5NwW+i2lB9HI30lSVET+/uz7NmiwnzIyGpJMZkUv/deQQA6KP/yanv/wAxWOd6LCiwoiX6JdW+fS\n9OK9VG9cPZ375eHtQTSUyEHhQAl3f6frCS+oR4+WVP/WQ6ItW0iyfj1rP2ECkZmZ0fu/68ULeh0Y\nSK6tWlHzTz+l2NhYcnJyIolEQs4KBdHKlSQZMIBowADqkWZCWW+diIiooOAY7dzZh1SQSCTk7OxM\nv078iM626kQX2jvRn3PmkTDnCU1xX08nPptEw0+fJhoxgiQNGuhcz+vXREuXOpO1NdH69RIKDWWf\nR72Oot6relNpYSn1K+lHFpMs6MytMzTcbDgN/HggkacnSYYOJapTh5yPH9f+fhcukEX3xvR25ltK\nbpNMzam57vPXti1JWrUiOnSInBcvNvh8eqd4032P9eSRRfRg5pe0z6kXbXu5jb4VfEsuA1xopGAk\nORY4ktkJC7r++XEqHnGQLK1L6da06xTsG6zub13/dTR081DaGrGV3NzcqMHkBlrn6x3YhfZ1P0UD\nfpBT2vYWNCVgIdlE2NBz+WcklO8kOnmSJN266f093V65kUlxTbJOzaOTJ69Sc6mEOq6dRatPfEee\nnhxd2XeFUu5lkrNbCMUJXlLOp0Mo/mot8o2KpxruDuQ42I5iQ6ZQUWwxiTZsJ+d27Yy+r/b2N0gm\ny6Ss5x8SJYfSxUaNiPvmG0ru0YPeGVW1MFXZiLmk7mn8XRmXVAwpXVJEJCaie8SMhbHzGLW01YXS\nUmbo31dGu1guh6W7OxbGxoLneTgoGT7B78iNV8k9t/X3B3EcbH4NAnEcXHzZqiJ2YSw8rD3Ay6te\n92DFnytAroS2+9uCXAkzr8+EJEmClLwUvSyqzMJM1N5WG5+c/kTturl+nU0a/SftwNZ+pNZY+mCX\nAwpbN2PyDnqWbTu9d+JEZ4K8Xl2j2dXBwb21FEJzc3NhY2OjVboTYWEsMcDMTJ0FGR4eDiKCgLbh\n98E74HmDEPGTNat7AGDy5cmot6MeatQ2xaj/1955h0dRtW38PukJoUjvRZDy0jsKKmIBERsqCCoi\nqOAniKCiiCV0VJDeRUSKKEUFpMOkQghJCIEQSkiAkJAQAiF9k925vz/OlvRCC8r5XVeuZGZnZ2dP\nZuaZ85T7eU7Qu/WvNGUVHixOPZHKiYMbEQD37Mnhi961S6pYFiN8F5uZyXJeXhxg/nyj0WgLJFty\nWv/3P6u0b8zSGGrQ6Ig2rFWrZ+E7NgdLHy+3l61e86HzZBc+vqI7TV26yJlAnkyO69flrKJChdy1\nmGExYXSd6Ep8Cg78v4HMysqyFo96n/cm9+yRcZrmzfMnKhQ2cyiIWeaU4LzpWGb2ndtH5ynO3Nq9\nKnV3d2uOb6oh1ZrSOvSvoUxOy2SfJ7PZ9MVXZZ1RlxmM/z0+l0vx/IzzbPFuC9b9pm6hUvApUZlc\nV+EgO77Vifbf2HNR/UVMDkyWujaNGxdY0RueEE54gH2mfcmdO8tx8+Za9Pd/kxejF3H8rvcJD7Dn\nLz05atwuarXWcd1G2UfG378Jr457hHRwYNKYp6ntA09tLL5lcWLiLm7dA47Z3JWnr57mg4cO8dV1\n66Q/0VwmjnvQJWUPW9DbCTLo3SLPNn1hC3p3gznobV7+FcCPJficYgfwTjFggHSl32rVd7/QUDY6\ndIi6rnP8+PFs3br1TTWyWbBtG7sHBVkb3v955QpPn9bpMiuU4m8f7vYyMm5dHDVoTAkpWkHx1Cl5\nr4yJsfWGsRQUwgN8+tenS3SMlor1LSe30GgkW7SQySrZN9Ko16jON0ZWJzzAjZ/2laekp2eB+4lI\njOCI5yC3KSLlMDz8HS5Y8IB12WTK5jRzltL8+fXo79+MBkO8LLAzawWljRvHwYMG0cXFhTvqvcLY\nvlIo8foleaO/ln6NTlOc+NGOj9j7mSfZoJ4d/db0KOwQSJLXr/uwfXuwdsWKNN3ECTLi1Ck6enoy\nIocoIUn5z+jYUd7Bc8S4wt4I43YXPzo4jLNWupMF9DfPzCRr1GB0276sVIlES6lJNnxKfymz3rOn\nVZQvM1NqFzo65vJmMDgimM7jnYnx4Kc/fGo9D1IMKXSb5saFX/eWgaG2bW3iRjmxxCZKotkSHS23\nLUD76VD0IZabVo5dZ7eg7uaW7+nNpJv4zYFvCA+wwthHiNbDCQ9w/PrxDOwkJTpCnw9lRnSGtUPh\n4uGLixWVfHeDTJP9tP2nXPHIOe7dSxp+kYV3eR8EIiPJ1l+MJL5yJsrFc+TInfTx6U9f3xpSMkQD\nv/rDlY6TBR+YWY6jf7Hjsk0OjDg3lSZTpsxeqVePBBixqLU5i67wuiiD4Qpn/lmJlafbER5g5e8q\n88VAjfW9veXxTZW90+85gyGPCX0gM5zOAvjCvG4EgPdzbLPQbFiOAWhvXtcdgMlsZI4CCAbQp5DP\nKHTw7jQWoclbFPrkYnN7zFNpsglPQc16iiIkJYUvHz9OzJnDmn5+XBoTk0tVc9Npqefv8Fo0ty1P\nlz0GFhdc35GQIGPIOZNTABlnrF2brPPsGrp+0ZgzFl/gtWsF7iIX2aZstlzUkg3nNuSylekEcghz\nzp/PLDswyON9eVMYVbR21WsTmsiD+a1w2e8LF77jnDlgTMwKhoW9Th+fSty9G6xZE2zWzJ2a5szg\n4EeZnZ3B/bt2cWjTpnSHTJkdXaUKTQL8e3kt/v13K+uN0JJjHxQbxInDJ5rjHODVqzvyfb7RmMZL\nl5Zwwx+1CYDD7d9m6snSBbpOpqbSXtP4Ud6n6pyS8nn6MGg1DvJbnOAbb+wwz2r2yPV5DQYpb74A\nUwJPccYM0rXvt4QH+NnDr5IA9Znf0WQiX39dflTOViCeRzzp8LEDMQH8Yf0P+XY9d1x3ZtmBpk6d\nCvbpWzJG8sY0iqJnT+rNmjHLoDM1Vd5Dgy4dY6WZldh4XmNen2+WOs7TMImUk8lqj/9BTHQl3gaf\nXfssjSYjTdkmXpx9kV6uXvQu701PB08efeIojRlGdljWgY3nNWa2Kb9ciqXmqMevI9hlpkbHrlcJ\nkO5OBiY61eCZ5v0YECAPZcAAUpS7Skx0ZZNPhuWaoem6zvT0CF6IWcVfj7zOCX/VZK2Ztt4q7pPd\n2XddX073nk6fvSuZOeEzGtOT6O/flAcPNsgl82EhPiWeTy6rJqVJJoPlpsm2CZVmNyT2budlSyq3\n0XhvGoy78VOWBsNS9f3NN7e2n6h02SHrx1IWdvjfuMHnQ0MJTWN5b29OjopiagHGRtd1dvQPotOm\nQ7RzMHJfRT+efOtknm1kRW61anLmOnGiXF6yhJw+XaaeDh8uK18fMss9ODnJYtdNm/J1qMzF/sj9\n8iT+4GE2f8bH5lHKzLQ+PbFRo2J14z32fsU0RzDtw4I1qUgyIWGb9cnN17c6w8Pf4ZUrm/jrrz8R\nAL/8ciAHDwZr1XI3B4jLc9jDD9PTzo6mSpWYtPtHahrYv/9SXr5MGk1GPvzTw2y1WBqQta+sJQDO\n+qE2Dx9ubk2BNRjiGBn5NX18qlDTwH5vVCHsBDfabeS5CYUEdQvhxdBQVvD25pX8WuFyrPLk6Kef\nz6AGjW9XiGZcXAodHBz4+eefF/4B8fG5mo+kpOhsP20g8Q240f1hZglHLm81l29gDf98YyO5bRuN\nu3dx56KJ7PyqYNMPwLUbZslsgZyzzNWrqdvZ0bs++E9gIUb98GH5HVautK66cUNKXqxbJ6+l11+X\nhYFVq8pC7A8clpMA2yNIPsBUPkO78TVYcVIdnoyNkjnRLVvmc1X+9ZfMLahVi1y9J4ij/hmVL2sv\n/Vw6j/U5xqBuQcy6Lv+Xf4b/SXiAa46tybXtrrO7aD/Jni/89gKvZmawxeHDdPH04je7EjhuHLms\n+lc0QbABogjIsqHHJk4rtIvlvmvX2PjQIULT+E54OBMy0+kf6c9RXUex91u92WJhC6sBcZnqwmfW\nPMMp+0dx5Tbw1Clbtauu61x6ZCndpjrQYRLYfp4TVwavZHpWOtstaSf3MbcjN/+5SY69uaEVlcG4\n+3TvTnbufOv7aXH4cJFyABZ0Xafn9et8KiRExih8fDgpKorXisjHJsnNV64QmsZWo+I5Cce5q8oh\n62sxMbI+CpDVrfl6UuQ7BlkQ+PHHUojRcnEMHy4v+p07yUOHpFsrPl6mir8+cxXxSS3CA3x+/fM8\nEW/uJLZ6tbQ8Bw4U+92DY4PpXR+Ma9O40G12nvmH9WZVYfXvK7PO7DpsMKcBm8xvwuYLmtNlnAsx\nAsQIsNxYsMHUquy0rBO7/dSNj8xvx44L2/DB2RVYY4Ygxlem/bcu1gv2e9/vZfplfY0OwoFjxrxK\nTQMjIsYzPHwYPT2dqGmCoaEvcu2R1US5chQ9evDHbp70qutXqOhjXrzN3d2m520YZVEEfvbZfH0c\n/h4t3Yy/fiOfOnv06MFOnToV/UHvviv3Z46VpWels+Oyzqz5uRsjHc1FcyX5cXSUd/YHHySFoKlX\nL9afWoUDNg4o+HPHjJHGKimJiYmyd1DO3Qkhnx1695ZalR9/THp8lMhsO0ce7P4Jv5wZzQcmNaDj\nl1WJquF8rPJxEmDmDFudga7bMnk7dy641rMoTLqJbZa0YfOFza2xubArYawwowLbLmnLFIN8sLma\nlcUugYG01zSuio0lL16kbmfHsBc+5/Ll5NXrBtaaVYtP//p0rv1fzcri0PBwQtPYxN+f+/NM1d9/\n/X1r+ntCWgL/Cv+LY3aOyWVAqkwHX9/wDFcGr2SrRa0ID7DpLHDW1tpMyrClsaUYUthoflOZFr/i\nKeo1a5D9+t2UwRCUN9x/NUIIluX3+PxzYO5cICUFcHK6+f18GhGBBTExSOzeHe4OBSewadev45vz\n5+F74waqOzri03r1MLJ2bZQ3b2/JhikIE4kWAQGoYOeAl4dXQ/fjkfD86BHUa+OETz4BDAZgyhTg\n44+BQj6+QIxG4MABYN06YMsWILXQXDagV+80PDlxHr7z+w6pWakY0nYIJvWchPr2lQF392I/iyRW\n9KqEoX6pcErNyDfguyJ24aUNL6Hm1Zro/WRvGHUjjDTK37oR129cR9yVONSoWQMGQyiyshPgXr4T\n7B0egE4dDoLISD6Ayu7NEX7sCZw9WQ4ff1gO9apWwrsd3gXDicB2gRjbcCwq1K+AefMckZS0H3Z2\nrqhZcyjq1v0Ybm5NUeOFF3Bl505sCwjAL1tTMcrDBJdtD6FbvzrFfr+Hg4NxyWDAma5d4WZvb3vx\nkUeAmBggJAR44AHran9/YGmvi3ghMxovZD4CBycBDw8PTJ48GYmJiTh27FjB50RiItC2LVCuHBAU\nBLi743LKZbRZ2BnJlwVaX3oJmdX+Buyj4WJwRN2UzsgIPIw+jR/H2KHDgORk4MaN3D+1agFTp+LD\n/Z/g55CfceXTKyjvXN72mSYTUKcO0L07sHkz5s8HxowBvv4aaN8eaNoUaNwYcHEpYHBefBGmIwFo\nO6ESotNiob2tIf1cB1x5Yyz6XVyEVg/E4u1PqmL4cHkO//478MYbwIoVgKur3EVR10deNoZtxIBN\nA7DhlQ3o1agXuv7UFenZ6Qh4LwD1K9a3bpdqNKJ/WBj2Xr+OWY0b45MxYwAfHyA6GmvPbMJbf76F\nHYN34NmHnkWmyYR1V65gQmQkrhuN+KxePXzdoAFcc/6fAYzdNhZdh3RF48aN0elIJwghrK9F34jG\n7ojt+D1wPAIS05GcrQMA3mjgjGGNXNC9WzicnWvl2l9SZhKqrXsXxkubMSq9NRb8cAJCGgGB0lBa\nC3Mv/qCMZxi//y6fZCzyMjeLpS/B3wUIHum6zh8uXKDQNNY9eJALoqOZXoDrqUB/dQ6WmvuJ7/tH\nSkt3RwIBGfstJAmlVKSny/RwPz9ZpLp2rewUNmWKFPW0lExcTbvKT3Z/QqcpTnSe4szP9nzGjOwi\nfFo5WPWlDI6n+mq51v9z5h86TXFi+6Xt+dfOv4rdT3Z2Eg8fbk5f36pMT48iSUZFTaGmgWlpp63S\n6B/naIIY5RFFTWgc/f5ouri48MaNCF66tJAGg+1/tnTXLgLgU+Yq7rNXU7jDTePEvp70KUKz6XhK\nCgeFhRGaxp9jY6nrcmaWkkJeCzxHArz44UyuXCmP6cknZVKT5cm8bzVbvMDb25sAuGXLlqLPiQMH\n5CO9ucFLXBxZpWUwxVdutJtkx6d+fYrTd/7MkWOv09nZgwDYtOlJbthQdKKHpRvh6pDVuV/Yu5eW\nIJauy9lFx46F7ycnaWtk46Wnhzna5NkzM8nKlXn1ydf43HO2GYoQUncwb05GcddHTky6iS0WtmCr\nxa3Y4+cedJ7iTP/ognvRZ5pMfO3ECULTuMLcp1tfvZodlnVg84XNeTYtleMjIljFx4fQNHYJDOSx\nItyv205vY58X+1CDxoS/ChZAu37dm/sOgAN+Amfv6EhNAxMSCj/v3zweTCzpTXiASzoJ5ZIqK86e\nlSP500/Fb1sUBpOJ7t7eHHEqtxZNlsnEEadOEZrG106cKNBQlJR0o5HVfH3ZLyCEno6e/P2pCP70\n061ned0sF5IuWPWquv3UrUQd/vz9/iABBn1p62K1/fR2Ok1xYodlHZiYXnT1a07S0k7T27siAwLa\nMDs7iQcP1mVIiM198M47MthvSeYJaBvA4B7B3LhxIwHQP0+QNTs7mxWbNaOoXp1xSbaq38AhJ7jD\nTWOl3Z7ckycQ7HP9OvuZ41Au80LoVtlIV1fdWoUOkF9C+lfq4zwBma1au7Z8rUX1TPZCHB3sdGvy\nmMFgoJubGz/MIz1SIBMnkgCNv/3BJ5+U3/efg5GMTbZlMKWlpbFKlaps06YfW7aUn9u2rSzALihR\nTtd1NpzbkM+seSb3C0OHyuyu9HQGBcn9LFqU//15Sc9KZ+9ljzLFCbwwoLftBcvT2u7dcpwDpe0r\nTFGjtKwLXWd1Af12vPBEC1L2/R55+jRx4ABjGzXijVZN6TCnC1t6b6PQNNprGvsfP859OfS/CuNG\n5g06fuPIf+r8w4C2AYW6MxftamGO1wmeOvV+gdtY+Ck2ljiwj87TK9HuGyiDUVbouvTf51RcvVle\nOn6c9Q4etJ5QSdnZfNocq5hw7hxNN5Fqm5fJUVGEptGnU4Bs43kPsPnkZrpNc2O9H+sxOLboYzIa\nsxlXXtD7sYYkya2nttJxsiM7LuuYL6BZEhITd1HT7Ojv38z8lGbLPjp3Ts4yPvqITI+U2WUXZ11k\nbGxs/qprkl/NmkUAfCXPXfDaASnJ8vbUg3Ty9ORfCQn8OyGBj5hToKv6+nJyVBQHvmlixYoyweCr\nr+TM7PvvdCbWaMHYJj24ebO8KVqepocMIY8PPsnNrofo7Kznyirt06cPmzdvXuj3Ts5MZuS1SDmN\n6daN3zrPyBuLtmLpy+3l5UWjUc4cGzeWx9Ctm03+Oydf7vuSdpPsbA8B6ekygj10KEkpo+XszGIz\n7bKMWXx+/fMUHoKR/brLRhCWCvmnn5ZZP3foicdoMvKF317g7IOzi9+Y0lB+HRnJQWYj/Mfjj7OO\npye/jYzkpWKq+vPyyMpHOGL4CGrQGL8xf2ry5ZTLLD/NkVv3V6S/fzMajUVn4oWmpBCaxmnhh1j5\nS3tlMMqSnj1losatstzsMjqRmsqo9HS2PHyYDp6eXFnCHqMlmXJfzcqim5cXFw45TC8XryKLz+4m\nwbHBrPtjXbpNc+Pmk5uL3rZLfZ6tYseNYRvpONmRnZd35vUcgb7SuB5I8sKFH6hp4MGDDajruWdw\nw4bJG9uq5y5Sg8ZdK9MYHEzWr9+IL7/c37pdXFwcncqXp+jcOV+/ad2k82C9gwzsE8IugYFWUcAG\nZvdimtHI7GyprffWW3kOLiREXqpLlvD4cVnz5+AgewOln8+gp4Mnz358lqNG5e4r8sMPPxCQvazz\nYsn8cpvmxrOJZ7n311gKmDik2j/Us3KnkhqNRjZp0oSdO3fO9WSclUUuX24TlX3iidxNxcKuhBEe\n4NxDc+WKTeYMnb17mZEh3WmDBhX+PzHpJp6+epqDN0mF48UBi2WjI0tK8fnz+Zu+FENpz4ubxeP0\nUY4ZKq26aeDAfEkKJeGbA9/Q4VsHHmx2kIf/dzhfoa2lviQ8PjCfdHlBGHWd5by8OPrMGXqe05TB\nKEs++URO5W+yy6WVaHODljdPnmR1X19W8vHJl0FRFCW9IEadOcNeHlJf50ZA8aJzd4vLKZfZdUVX\nwgOc4jWl0Kn7yXFDSIAPjAe7rOiSy1iQpb8x6LrOCxe+Y2JifjHAqChZFD4HwVyJgBwZPW8SqMEO\nHXQmJZED3nqLcHDggEIquM99cY6avcbES2kcc+YM18bFMSvHk7Gmyf1uzmsrx48nHRy4aWkCy5WT\nhaK+vvKls2PPUrPXmHE+g9HRMtnM0gU3ODiYAKxtZXMy99BcKa892ZGdZ7/IatV0/q9OElPhli9l\nd8uWLYUaHlKmU8+dK/XwnJ2l4KyFdkvbsfNycwph//4ypc5olBpnKHhmQkqZ+xfWv2B1B9WeXZsj\nt43kSv+lzK78AE0DXpOGQojcnbeK4W4YDF3X+dofr9FxsiOTpnwlv+hbb5XaaHid9yI8wO2zt1OD\nxrj1toZcGdkZrPZ9NfZb369U+3w8OJhdzUrCymCUIZZ+28Wlo5aE1gEBhKax0aFDDL9VZcNCiExP\nZ/U/pMGInhd9Rz7jZsnIzuAbm98gPMBBmwZZ5aZzYtizkwQ4ZkwzJmUUrhB6uzAkGKjZaQz6MJIH\nD8peQIMGSTeNEBF85RXZfhWDB/O0ucI6L6lhqdKlNedivvIF0pZtmisWajLRVKceg2o/R4B85BFb\nimjWtSx6u3sz7I0w6+YffCCzXC9eJE0mE6tUqZKrJzhJRl6LpNs0Nz637jn+dOQXor4XnVyypJbd\n22/LwiIvW8/vhx9+mI0aNWJ2MU9DMTFSZf6VV2zrfvD7gfAAz0QGyi83ZgxJ6Ulq0KBgT1JGdoat\n46QH2Gl5J/ZcJSX04QEu7AymOYJJVd3JZ57Jv4MyZvZBKZk+3Xu6XGHJ7x02rFSuM4PRQLdpbhy1\nbRQDWgfQv6k/TQb5/p+CfiI8wP2R+4vZS24+i4igk6cnDSaTMhhlyalTcjRXrbr1fa2KjWX/48fz\nF23dZgaeOMENNTX6VPVhxGcRRfb6vtvous7p3tMJD7DJ/Cac6jWV567lKH5LTqYuBE1PP52rIc6d\nwtIPPTnIVl0bGhpKAOzVayUh2lBUr87ni2n0fqTjEXq3OEI3N1nvsmWLvIfoupzF9MvzwBgwy4sE\n+KbdOk6ZknsGe376+XwSLxcuSIPxf/8nl1999VXWrVuXBoOBly9fZmhoKDt+2ZEug104c95MDhgQ\nIUspXh3KUwmnpC5VkybSz5SYSD8/PwLgggULSjROkyfL68DLS7qUdp7dSeEh+NRY2WL3mucuqyfJ\nwyP/+9Oz0vnMmmcID7Dq91XZZUUX6yzTpJt45uoZ7ln9LS3TvJiVc0t0XHeLA5EHaD/Jni9veDn3\n7Pjbb+UxjxhRpA5aXvqs7cPmC5vz6var1n7nuq6z1eJWbLOkTanlgzbGxxOaxiM3biiDUZaYTLKi\ntBhliztOaabcgcnJbL5Y45ZnDtPTwdPaMe7S4kvMulayBkulwXgTAfvtp7ezx889rE+bD//0MBcc\nXsC4lDjZ9tDZWf588YXshmTmdrseQl8M5cF6B3NdoCaTiRUrVmS1atXl7MLDg9wTaKgAACAASURB\nVL7Xip7tRHwn05k7Vkm1Bo1btJDBbUB2SSRlG5DRo8klGME04cZg79w+amOGkb41fBnyTP5Cz/ff\nl66p6GhbsLrgnxcIkA8101hpaiV2+6mbLFI7ckRanSee4EvPP8/KlSsztYQz3YsXL7Jbpx/4+tO9\n+OWL5TmnK9h6JNj4I/BMZbDyzAf4gsdKQuj5PEmphlT2Wt2LwkPwva3vER7I1Xwrx8DTWL8uE9zA\nDzYPy/96EdxJl9TFpIus9n01Nl/YPFfPGJLSSEyYIP/Jo0aV2GjM8ptFeICXblziiQEn6Onkyb17\n9hIe4Kqjq0p9jBfMLu+Fly4pg1HWPPqodBmUJaW9IJ44epR1Dx5k6uUMXvzxIgNaB1CDRk9nT54Y\ncIJppwt2r5SWxKws1vHz4xc5G+iUgvPXz3Omz0y2XdKW8ADtJ9nzmTXP8EzQXtlfApDVxgsXkllZ\nt/XGkJ2cTS9XL54ZfYa6rvNyymXuj9zPBYcXsF5HqSzs2LELMSeo2A6MIwYYuA8atUERzM6Wklg5\nK52nTZOd4Jo1Ix1hYKpLZWYPyB8ZjlkhlWmv7csf34qKksHv0aPJGzdu8M033+TkyZM5/cfpdB3k\nyjafteE335ynvb3OGjWiCbiwcevGxFhZzU6SXLuWp4WgAPhVURIjFgwGnnr1CZpsAR4SYJarM5f1\nk9X921Z+zkd/flRqG419jOEJtt7yKYYUPrbqMdpNsuMvR39hq8Wt2HJRS5r0Qlw4msb5k/vRaYoT\nY5JLXsZ9pwxGRnYGOy/vzPLTy+f6XrnQdRnsBKQkQl5RyQIIuRxirWcxxBno84AP1zRbw5rf1WRm\ndumyruQh6Kzh68shJ08qg1HWjBkju4feQpnEXWf71auEpnGdud2krutMDk7mmY/O0LuiN73KeTFu\nbVwxeyme7y5csGYGLb5UsOhhSTkRf4IT909kpZmV2HedueVhYKBMVQPIpk2lr6c0/4jwcBns3Z/b\nJ6ybdB567hAP2B3ggIkD+MDMB6yzHXiALn1dCEc7YvVqthmZwIoVZfFbQZjrubipyTEerHvQmltv\n0eIrX952r61blzw6ZZtc2L493zH5N/XnkQ5HCnVJDB8uJ16WeIeu63zxtxfpPMWFH4xLJCClN27c\nIDdt2kR3d3c6VXCi4zuODLsiYyIjevWiE8C47t2tnQ8LJCGB+uNS9XfjY1V5Zv4kvvM/X7auEc+U\nZJ3XM67TaYoTP9j+AffsNREdVtBtciU6TXHit9q3vJJ6hd1Xdqf9JHuuD13Pv0/9TXiAa4+tLfJf\ndu7aOdpNsuNnez4rcjsLPhd82HVFVwbF3lzbgKKwzIi2nNxS9Ia6bq17YatWZFhYkZubdBOrfl+V\nb22RqXPBC4KpQePysctv+lifDw2VrQ+UwShbLDeEYs6BewqTrrOZvz87HMl/88mIzmBwD3mChr8T\nTmPqzVnCbJOJ9Q4e5OPBwewXGko7TeOOq6VrEZuT6GhZ7NW420mKV95kfKo5R13XZSVZ8+byH1G9\nuvTP7N5dcN/jlBTZc9vS8hWQ7zWPw/nr5zl3wFxq0Pj6CyPZac3LfGfbaM47NJ/7zu1jbHIsDQYD\nq25aTWxfxcn//EQnJznhycvp0zIg/OijZOxaqfsUsyKGui5dM4CsTPbykk30rl2jzDmtUiXfsV/5\n84rMzd9QgGy4GUv9iKVK/fcTvxNfObH902EEpIxUzt2Gh4fzoWYPEQKs+0pdxlyOoYuLC9/t2VMG\nHJ54omCjceIE+eCDNDo5cnB/cFOYlCH285PfyZJw9f7W92k3yY7PDPNnpUpkVEIcB2+W6bJOU5zo\nMNmBG8M2Utd1dl3RlY3mNipQKTYvgzYNovt092Lrb9Ky0vjgvAfl7GZmJQbGBBa5fWlYHric8AC/\n3Pdl8Rtb2LVLqny6uko/ZBEuqoEbB7L27NrUdZ0jt47krMaz6FXeixnRJVNGyMsUcx2WMhhlTFiY\nHNFffy27Y7iZKbdFLsSzANkKU7aJkV9FUhMaD7c4zJTjxed752WTWfTwr4QEpmRns/2RI3T39mZI\nMcq0FnRd3pemTpWBYsu93b28kRDZHPljHj93djY1Dw9y4EAZWAJk0v+QITJ/389P3jEtrzVtKu/W\nM2eSAK/u28ZR/4ziU689RQ0av+/zF3FAs86QHD09WcfPj+2PHOFjwcGEpvF/m6XMyTtfHSaQW0cx\nM5Ns107WWERHk8Z0I4+0P0INGo8+cZQ/fJ5JIFdrC2nM3NzIkSPzjUfQw0E81PAQTdlFZ9wMHSpT\nvVet+5tVPB6i+0NS6XX69ILvT8nJyezWuxsBsGL1igTA8PBwqeFfkNHYvl1Oi2rU4Idfd2S9H+vl\nuskPHCjvhxcvysrlurPrU4xuyvf+z7aP3RG7+diqx/hXuJS0OBB5QEpXHFlS5HezYHHZTPOeVuR2\nn+z+hPAAv1jxBRvMaXDbjIZ/tD+dpjix95reBTYQK5LYWKnvAsjBSio4/rUiaAXhAfpe8KXrVFd+\ntOwjerl5MbRf6E31zNmTmKgMxr2A0Siv8ZzaQ3ebggyGySRdD4WRbjSyio8PXygiJzhxbyJ9a/jS\ny8WLMctjSnWiPhoczIaHDlmD3pcyM1nHz491Dx5kTBHVr7pOLl4sk3YsRqJbN3LGDOlBSk4mXeud\npJ1zGgPzXPvWcUhPl0ZiyJDcwktubvKO6uNjvXsmxp9nposjV3W0Z4v3W3Cv016ua+9Nx91SenrN\n5cucffEiP4+I4Dvh4Xzu2DF2DgzkUyEhjEm5woZzG7LO7Lqs3yKezZvLjoykrBIH5OTHginbxEsL\nL9Gnsg/b4xobV8qkIT5HVtzatfJNOfqak2SSb5JMhV5QfCr02bMyQ7ZG6wVE1XA6Opm4fn3R79F1\nnW2HtCXswCf62LoW5jMas2bJ5XbteCpYBmFn+szMta/z56Vb7I035PKYuVLiftDqMYV+/lO/PsWa\ns2qWWFeMJJ9d+yyrfV+twPRrkjx86TDtJtlx5LaR1DSNUdej2HBuQ1aaWYlHYo6U+HPyEpMcwzqz\n67DR3EalkqPJhdEoLbi9vVT7LaCxTuS1SMIDfGj+Q4QHGBoXyouzLxY7y6TJJDVSknP3zbiWlaUM\nxr3CI49It8O9xJgx8um2CN07fh0ZSaFphdYQkKQhzsCQp0OoQWPYoLASVYgHJycTmsZZFy9aZc5J\n2fDJ3cuL/db689TnEQztF8qr/1y1GqLUVHLwYHmG9uhBLl1asET1N38vISpGsWr17KKa8Jm/gEG6\nAtasyWdBE9MT2XBuQ/7cDsxwdqR39Z38s5YXK23ROCkqqkQGMjg2mC5TXdh6dk/CLpuDB0t5D8Ba\nfpCP+Mgs2gudb4gL9K7gzQs/XKAp00T27Sv7hOTJ2w99IZQ+VXxK7B58pJ9Mm3Upn5bX9hRKQloC\nK39emR3nd8wddLYYDYuIVf/+ZGoq39/6Pl2muvBqWn43oyUx6PBhOTus+tZowgM8EJlfyj7gUoBV\nRr40eEZ5Eh7gooD8olQGo4GtFrdi3R/r5spculWjEZscy2YLmtF9ujuPXj5a6vfnw89PSpw4OOSL\nWZG0utOe+vUpkqRu1BnYOZC+1XyZdbUAd2tCgpTBt/gf89DU318ZjHuBUaOkp6OsxPzycuwYrSJ2\nM2YUvl2cwUAnT09+kMsvkh/dpDNqShQ1aDwzqnh523fCw+nm5cWwqCy6upJNm+r8bW46I748x/0P\n+lGDxv32Gn1r+FKDxpCnQhiyLZWtW8t709SpRY9lTHIM8WELupRPY7NmsqFVadF1nS9veJmOkx15\ndP1CEmCo02dsslKqxpaGX0N+lX0H3vbIFRaxTKTSs9K5PnQ9B20axKDYIGvHRm1DOo89d4waNB6u\nuZ26sOe1ju/x0sJLvLrzKtPOpjHlWAo1aIz8pjjLKNkYtpFibAPWfGQPQ8NKV9Nj+R7LApflfmHN\nGjlt+Oor0mTitfRrdJ3qyuF/Dy9wP8nJsrjbMkv8YW4aH5r/EBvMaZAv9fTlDS+z0sxKTM7M30mu\nKHRdZ7efurHh3Ib54h6TPCfJaunT+W/C56+fvymjEZcSx+YLm7PctHL0ueBTqmMtkmvXyPbtpVZW\nVFSulyxB9X/O2FQVU46l0NPBkyffzt0IjT4+ZJ06Mrf64Yfl7CWPFPW49SHKYNwLrFolRzWP4Oxd\nI6dLStdl4lDlynLmU7Om7cZVEMPCw+nq5cWrxTRiIsmz485Sg8bYnwq/oV4xGOhsNkITv9QphM76\njrJFaztc429dTnPdd2Gs8JfG0SdOM2rORc4sF8ZyyGZFZyO3rS/ZTe7J1U+y9kcD6eyss3t3KVVR\nmljOooBFhAc4y3cWD74SwlTU4/H6rbjzJgPzo3eMJjouJYSRQpANG+rcFebLd/9+11qtDA+ww7IO\nfOVVnbVq2Yxi4q5ExrST05JAl5+pQcv14+XiRcOV4sdl++ntdJjswO4ru3PHnvxtZItD13U+tuox\nVv6uMhPS8shr5zg/LJXcIZcLb/y1YoW8JpycpEH3u+hHu0l2fPdv25OvRXfq6wNfF7qfovgr/C/C\nA1wXausleyL+BB0nO3LQJltact7z4vz182w0txErzqjIw5eKLrokyfjUeP5v0f/oNs3NJrF+Ozl3\nTiqZdu6c62K1ZAbmTTM+N/EcNWhM3J0oT6IZM6SBaNJE9luIi5Pu18GDre9JPZHKvRW9lMG4Fzh2\nTI5qzh7Id5OcF8QfUgWcixfb2hAUJcF+3KxmObUYbZ6VsbHsGRBE/yeD6enoySS/goN1U8+fJzSN\nwZeSWdkpm92RwIDHjnLa69dZtYpOIWRo4V3vSGKfRue3L8hCsqrp/M3hEL3KeTFqUlSx7pdVR1cR\nHuDUJacJSGmK/fu1It9jIeRyCJ2nOPPZNc9S+/wkNWjc2HWkHKyTJ4vfQQGcPJVF2GXTrutiPjNh\nCSFMRLuVLDetHN/+820eiDzAtcfWEhOd6eyaZdV+stKjB9myJXWTiZmxmbzuc52xq2J5buI5xv9e\nhM/azP7I/XSe4syOyzoyKSPppmsPTsSfoMNkh0JnD0aTkQ3nNuRjqx4rcj9Go4w9vfOObd3nez/P\n9cQ85M8hdJvmlt84lRBL7wpL9bPRZGTXFV1Z5bsqvJJ6xbpdQWNhMRr2k+w57K9huRUFcnAl9Qpb\nLW5F16mu1KLy7+e2sWULrQV+xWDMMPJw88M8VH4rs7rkCKDndLl+8YWcrh8/zvSodPrV9qNXTV9l\nMO4FsrNlZsonn5TtcaSlSZdo27bygtV1Odtt1qxoF0/vkBDW9PNjZiEbfZ+jnqLjHn/6NT5Ev5p+\nzLyUe+qSZTKxtp8f+/kd5aQWsofDb/9nu3CTkqSmnpMT6eqqs0nbbClR0fcyscuLLTZ485dnDlKD\nRv/m/gX7ac3cyLxBl6ku/PCfD/njj/KsLkniQaohlc0XNmed7+ow6N2j1KBxWl9vno+MlL7kTz8t\nficFMGgQ6epmYo1v21J4CDZ8YQ0B8pe1tkCuruts/tE4AuTmrTmqqENDaa3guwn8Lvqx3LRybLW4\nVYExhdLy2Z7PCA/w4MWD+V6zPNVbUmmLIm8IKDM7k60Wt2KtWbUYHBtM+0n2HLtr7C0d6y9HfyE8\nwB1ndnDOoTn5ZhxFEZ8azzE7x9B5irPVSEZes7n+EtIS2GZJG7pMdSm1ftNNMW6cPA82bCh208zf\n99DgUI0mODJp6Mz8g52YSFaoQNOzL9D/IX/6VPJhyvEUZTDuFbp0ka6gojAapTrpnSrys0jX5NCQ\n4/r1ct3fBagtWNhtTrlblcd3r+s6J5w7R2gaB544wb2JiXT29OTzvx+ml7s3AzsH0phh+zK/xcWx\n4p8a97b1Z1Mks2mdrAJTOSMjbemXS5eSGUYTtyYk8M2TJ1ne25udvte4x0mjT7cjufafl4EbB7LK\nd1WYZczixx/L7zlzZqGbkySH/TWM7p+788CjB6hB44iBGvclmLNdXnpJ1nGUwD2XE4sS+YQJ0td9\n6cYlZmdLV3KFCrld0y8NjiecbnDayg9l8UXXrvLNrq75fNglISg2iBVmVGDTBU1L1IiqJKQYUlj3\nx7psu6RtvvhAr9W98qXSlobg2GA6THag+3R3Ok52ZPSNWxPBNBgNrPdjPbZZ0sYqrljatNOY5Bh+\ntOOjXIYjMCaQ7Za2o8tUF+49t/eWjrHEZGXJk8bdPU++dQ6uX5d1RgD1B5vwVMcNufSmcmKc6EEC\nDHJeavUIKINxj/DBB/LmUNST/Pffy9F/8UWZEXS70DSN58/LWc7Agblfy86WCqHduxf+fl3X2Sog\ngK0DAnKIvun84PRpQtP4/qlT1vTYP69coZ2mcfQcWVNw8q2T1vf02X6E6xt4cpHTUQLSGBRFQYYz\nw2jkxvh4vjTFhxo07ng+sNDOY9tOb5PyE6e3MSvFyEdb7yZALltW4OZcF7qOtT6qxe31t9PTwZMj\nvzrI/x0+bLvQtpmrrLcUU7mbh379ZPZuXkX6qCh5Tjz8sPw/mM5EcIr7DB4rZy4yBMgOHWSKZU59\n8BJyPP44q3xXhQ3mNODFpIu5XrtVOYxNYZsID3Ce/7xcn1dQKm1pmew5mfBArnjGrWCRbS8/vXy+\ncSBLPhYxyTEcvWM0nac4Ex6g8xRn7o7YfVuOscRcvCgLN1u3zl80uXkzWauWzGgZN45MTaUp08Sw\nN8KoQeOp905Z63SMGUYe6+FLAyrS0MGWKq0Mxj2CJchn6V+dl+RkeR48+KD8f3fqRF6+PQ+E1DSN\nr71mK5jKy7x58tj8/Arfx8+xsYSmcW9iIrNMJg4295keHxGR78llhbnob9aHUoPq4o8X6X8knr9X\n07ivvBdf7mVgpUq3ZhRjMzM5fuwhatC4YviRXD0kLGQZs1jluyocMXcEA1oFcBbmsBuuUkDnso+T\nZKqqmbOJZ9nl/S7c7r6dPg/40HtrNKFpXJJTsiQ7W16Qzz1X4uP09aW1MK4gfvuNrIHLPNJuOHUh\nSICXH+zICX0cOXJB74LfVAIS0xNZe3Zt1p5dmxGJ+Y3NrRoMXdfZe01vVphRwdq2tahU2tKQZczi\n4oDFNx27yEuqIZWP/vxoobIipR2LSzcuccK+CXfHDVUQu3bl6rnOS5fk7BeQ1aBHcmd36bpuDYQf\n63OMWdezePzl41JpefC3zOl2UAbjHiE4WI7s778X/Pq0abTmpm/dKpMY6tcnjx+/9c8+cEDue/Lk\ngl9PTZVZUy+9VPg+Mk0m1vD15ZNHj1p7Tc8oIhA+7fx5iv0a1z3jT81O464KntxSWWPQ9iTa29+e\neI7BaORPb0qj9On4Q4wrQPp95iczucNpB32q+jBubRzDPotkO6ck2sPEH9xP8MxHZ3gt8BrfH/o+\n99jvoW9jX6adSePAEydY0dubKXn7PUyYIC16CbSvdJ187DGZQlqgcczIIKdPZ7qDOw1w5O/1xrGR\n/QVev05O8ZpCeOCmA6nvbX2P9pPs74hGkoUzV8/QaYoTB28eXGwqreI28/XX8qJ+5x05TXVxkcoE\nRbhLY5bHULPX6FNJzs6j50bLItbatWVSha4rg3GvYDDIYO748flfS0qSadY5+x4EBcmH2QoVyD17\nbv5zs7Pl7LVhw6KFML/+Wj60FJX6a9GbESUQC9R1nR+dOUOXHRr/au7L9bU0Tth7khMnys8ptqCu\nhOhGnTt6H+E+O43Pz/ThIbOUgjHNyPDh4dSgcW6DuVyze431PUnXdLZpkk0XexPnOxy1pqfu6bqH\nWYlZjMnMpIOnJ8cWNB08e5YEmDZxGpcuLXzGSMoHQYDM1zZC12XgskEDEmB2v5f4VIMzBMinZA0W\n07PSWX9OfbZd0rbU8hK+F3wJD/CT3Xc+y8LSEvSlDS8Vm0qruI0YjWSvXvIEe/LJErssr+64Sp/K\nPoz8NscFuHix3M+OHcpg3Et07Cj/t3nx8JCjHhyce/3Fi/Jm7+BQdOprUSxaRAIaNxWTtBIfLx9S\n3nuv8G2uZmXxiaNHub4w6dU8mHSdg8LC6Lhbo+NujccT01itmozR3E6MaUZ6dwrgLmeNrZZoHPL3\nUf75kA8PCI0bRoew5sqB7Pj7MG7YbfM3X7lCNnoog3bOyezV/ROuGbXGWqVuqXCPKMDC6jp5ufnj\njLRrTAETHRzIDz/Mr0ar6zL80LChTQ6EGRlS9NAibNi2rVVgKihIjv/KlbZ9bDi+gfAAlweWXIXU\nYDSw5aKWrD+nPlMMhety3S5J7/SsdDaa24jwAB9f9fht2efd5m719L7t3LghlZRLGcTPF/MzGOSJ\n2qGDMhj3Eu+9J2cSOf+/167JWcTLLxf8nhs3pOQ0IPWHEkro1tV12Ru5cmWyfXutROfUyJFyFnS7\nYickaTCZ+HpYGN8/dYq//CK/x/474Po1xBvo1+ggd1by5C5XjX9X0tjlO82a7gtNI+bM4Wrzl1sZ\nvJLOnzahfaVoVqpisM6sMk0mVvf15XPHjuX7jFOnpGzSm5ASxEGzNX7wgayJcneXht+inbhxI2kH\nI7d5BMrUrKeflhYBkD6qFSvyRfWTk3OfG7qus8fPPVjt+2olbjlr6Ui47fS2Ire7nTfJHWd2UHiI\nghsb/Qv41xqM24n54lQG4x5i6VI5ujndMRYZ/ALuT1aysmR7TUDGNsaMKbwDqa7LZJ5u3eT2tWuX\nvNbszBnpLvqyEEVmk0m6YGJicrcFLQmWmo+WLUv9QFRi0k6l0beaL4MfC2bmpUyadJ1XDAZuvXSC\nmNuBD3pupYuXJ5/fOpbwAJ9c/SQPHk1g9epSZrx3b/K1L5KJ+UHcdtkmHJeRQX7zjTSmFSuSK+al\nUa9QwapZfvo0+eqr5ANIZP9K++n78izuLP8qr9tXpjXbqVUrWQiybVupov2BMYEUHoKf7i6+/iMi\nMYIuU13Y//f+pR+8W8QqJ6/4d2I0ks2b35sGA0AfAKcAnAHweSHbzAdwFkAIgPY51q8EEA8gtJjP\nuM0jeuscOSJH1+IeSkiQT6YDBpTs/SdPSjFVBwf58/bbtj4bRqOs4m7bVn5GgwbkkiXyZlcaXnlF\npoAmJ0tD5e8v032ff17Ojiz3Pzs7KSvSvr3UxHv3XfkgXZjMkiVbqLhU2lvFmGEsMM++8/LOfHBx\nRzrs2ULsWMfPDky2xgbCw2Xac8uWtu/n6qqzVy9p0C2aR2+8kcP1NGKEnDF8+630sZnjEZaf86jP\n873ekeX9tzhlG/rXUDpMduCigEWF1hBYspbKTy/PSzdurRmV4j7ljz/uPYMBwA5ABIAGABzNBqF5\nnm2eBfCP+e+uAPxzvNYDQLt/o8HIyJA3+gkT5PL48fKJvrTNlS5csHXyA2SwvFkz+XezZnJ2mTNZ\nojRTbn9/uZ///c+2f4B86CHZsW3FChkj+/praST69pVGo2ZNuZ2jI/nWW9Inn5MBA3jLqbS3wjz/\necTbYMVFD9NBO8C+x47RlOfme/jGDeJPXw5fnsCPPpIZikLI775vX54dBgXJF4WQvTMGDiS/+476\n7j3cvfYKZxZQXHuzJKYnsvea3oQH+Pz653PJWlj47fhvhAc4339+ifap3DA21FiYMZnuSYPRDcDO\nHMtf5J1lAFgKYGCO5XAANXIsN/g3GgxS3oR697bpf1n6AtwMCQnyAbdqVbnfP/4ouNittBfEoEFy\npjJqlNxnSR+Qz56VcRZLD6JHH5W1RBcuSD//Tapq3BZSDCkcNncYo29Ec/GlS4QmJcpzYqkkT87h\nb0tOLqLyPirKFrS4w5h0E+f5z6PzFGfW+KEGd53dZX3tWvo11vihBjst71TijCp1k7ShxsLGvWgw\nXgGwPMfymwDm59lmG4BHcizvA9Ahx/K/1mAMGyZv8GPHSrdOMcrh/0qSksjZs21eGlfX25tKe6vo\nus4hJ09S5GgLezkzk46enhx9pnh59rIkNC6ULRe1JDzAj3d+zIzsDI7YNoJ2k+wYHBtc/A4UiiK4\nGYNhB8Udo2NH4OpVYMECYMgQoGnTsj6i20/FisC4cUBEBLB5M9C1K/Dhh0CjRmV9ZBIhBJY0bYo2\n5cphcHg4IjMysPzyZWSTGFWnTlkfXpG0rtEaR947gtFdRmPu4blot7QdlgUtw5iuY9C+VvuyPjzF\nfYjDHd5/DID6OZbrmtfl3aZeMdsUy9ChQ9GwYUMAQKVKldCuXTv07NkTAODp6QkAd325Qwe5rOue\nePppALjzn2/5uyy+b//+PdG/v1z29Lz7n59zOSQkBB9//DEAIMDHB58ZDBhVrhxeCQvDRX9/dHZx\nQdMyPj9Ksuzq6Ir+rv1Ru3FtzImbg/oV6+Npu6fh6elZ4v3NnTv3nrge7oXlsrw+ynrZ8vf58+dx\n05R2SlKaHwD2sAW9nSCD3i3ybNMXtqB3N+QIepvXNQRwvJjPud2ztdtCerqMXbz//t37TOWjlRQ0\nDtuvXrXWaWy/yeZIZcmNzBs3pd2kzgkbaixs4CZcUkK+784hhOgDYB5kxtRKkjOFECPMB7vcvM1C\nyPTbNADvkAw2r18P+VheBTK99luSqwr4DN7p73GzREQA9eoBzs5lfSQKAJgbHQ0tKQl/tmoFOyHK\n+nAUijJDCAGSpboI7rjBuBvcywZDoVAo7kVuxmCooPd/jJz+yvsZNQ421FjYUGNxayiDoVAoFIoS\noVxSCoVCcR+iXFIKhUKhuGMog/EfQ/loJWocbKixsKHG4tZQBkOhUCgUJULFMBQKheI+RMUwFAqF\nQnHHUAbjP4by0UrUONhQY2FDjcWtoQyGQqFQKEqEimEoFArFfYiKYSgUCoXijqEMxn8M5aOVqHGw\nocbChhqLW0MZDIVCoVCUCBXDUCgUivsQFcNQKBQKxR1DGYz/GMpHK1HjYEONhQ01FreGMhgKhUKh\nKBEqhqFQKBT3ISqGoVAoFIo7hjIY/zGUj1aixsGGGgsbaixuDWUwFAqFnjQhQQAABi5JREFUQlEi\nVAxDoVAo7kNUDEOhUCgUdwxlMP5jKB+tRI2DDTUWNtRY3BrKYCgUCoWiRKgYhkKhUNyHqBiGQqFQ\nKO4Yd9xgCCH6CCFOCSHOCCE+L2Sb+UKIs0KIECFEu9K8V5Eb5aOVqHGwocbChhqLW+OOGgwhhB2A\nhQB6A2gJYJAQonmebZ4F0JjkQwBGAFha0vcq8hMSElLWh3BPoMbBhhoLG2osbo07PcPoAuAsyQsk\nswFsAPBinm1eBPArAJA8DKCiEKJGCd+ryENSUlJZH8I9gRoHG2osbKixuDXutMGoAyA6x/Il87qS\nbFOS9yoUCoXiLnEvBr1LFbVX5Ob8+fNlfQj3BGocbKixsKHG4ta4o2m1QohuADxI9jEvfwGAJL/L\nsc1SABrJ383LpwA8DqBRce/NsQ+VU6tQKBSlpLRptQ536kDMHAHQRAjRAMBlAK8DGJRnm60APgTw\nu9nAJJGMF0JcLcF7AZT+SysUCoWi9NxRg0HSJIQYBWAPpPtrJclwIcQI+TKXk9whhOgrhIgAkAbg\nnaLeeyePV6FQKBSF85+o9FYoFArFnedeDHqXmPu5sE8IsVIIES+ECM2x7gEhxB4hxGkhxG4hRMWy\nPMa7hRCirhDigBAiTAhxXAjxkXn9fTceQghnIcRhIcRR81h8a15/340FIOu5hBDBQoit5uX7chwA\nQAhxXghxzHxuBJjXlWo8/rUGQxX2YRXkd8/JFwD2kWwG4ACACXf9qMoGI4BxJFsCeBjAh+Zz4b4b\nD5IGAE+QbA+gHYBnhRBdcB+OhZkxAE7mWL5fxwEAdAA9SbYn2cW8rlTj8a81GLjPC/tI+gK4nmf1\niwBWm/9eDeClu3pQZQTJOJIh5r9TAYQDqIv7dzzSzX86Q8YpiftwLIQQdQH0BfBTjtX33TjkQCD/\nPb9U4/FvNhiqsC8/1UnGA/ImCqB6GR/PXUcI0RDyydofQI37cTzMbpijAOIA7CV5BPfnWMwB8Bmk\nwbRwP46DBQLYK4Q4IoR417yuVONxp9NqFWXLfZXRIIRwB7AJwBiSqQXU59wX40FSB9BeCFEBwJ9C\niJbI/93/02MhhHgOQDzJECFEzyI2/U+PQx66k7wshKgGYI8Q4jRKeV78m2cYMQDq51iua153PxNv\n1uGCEKImgCtlfDx3DSGEA6SxWEPyb/Pq+3Y8AIBkMgBPAH1w/41FdwAvCCEiAfwGoJcQYg2AuPts\nHKyQvGz+nQDgL0i3fqnOi3+zwbAWBQohnCAL+7aW8THdbQRyS6lsBTDU/PfbAP7O+4b/MD8DOEly\nXo519914CCGqWjJdhBCuAJ6GjOncV2NB8kuS9Uk+CHlvOEDyLQDbcB+NgwUhhJt5Bg4hRDkAzwA4\njlKeF//qOgwhRB8A82Ar7JtZxod01xBCrAfQE0AVAPEAvoV8atgIoB6ACwAGkPzPy3MKIboD8Ia8\nAGj++RJAAIA/cB+NhxCiNWTw0s788zvJaUKIyrjPxsKCEOJxAJ+QfOF+HQchRCMAf0JeGw4A1pGc\nWdrx+FcbDIVCoVDcPf7NLimFQqFQ3EWUwVAoFApFiVAGQ6FQKBQlQhkMhUKhUJQIZTAUCoVCUSKU\nwVAoFApFiVAGQ6EoJUKIikKID8x/1xJC/FHWx6RQ3A1UHYZCUUrMAofbSLYu40NRKO4qSnxQoSg9\nMwA8KIQIBhABoAXJ1kKItyHlocsBaAJgNgAnAG8ByATQl2SSEOJBAIsAVAWQDuA9kmfK4HsoFKVC\nuaQUitLzBYBzJDsgv3x2S0ij0QXANACp5u38AQwxb7McwCiSnc3vX3K3DlyhuBXUDEOhuL1o5gZG\n6UKIJADbzeuPA2htFn57BMBGIYRFONKxDI5ToSg1ymAoFLcXQ46/mWNZh7ze7ABcN886FIp/Fcol\npVCUnhQA5c1/i6I2zAvJFABRQohXLeuEEG1u47EpFHcMZTAUilJC8hoAPyFEKIDvUXiXssLWvwlg\nuBAiRAhxAsALd+AwFYrbjkqrVSgUCkWJUDMMhUKhUJQIZTAUCoVCUSKUwVAoFApFiVAGQ6FQKBQl\nQhkMhUKhUJQIZTAUCoVCUSKUwVAoFApFiVAGQ6FQKBQl4v8BUr+x+nS3X04AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa8610b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x1[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: srd_dt_Euler\n",
    "# title: Simulated square-root diffusion paths (Euler scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "uuid": "b901c93e-a4a9-4f8f-98d9-69754cb586bf"
   },
   "outputs": [],
   "source": [
    "def srd_exact():\n",
    "    x2 = np.zeros((M + 1, I))\n",
    "    x2[0] = x0\n",
    "    for t in range(1, M + 1):\n",
    "        df = 4 * theta * kappa / sigma ** 2\n",
    "        c = (sigma ** 2 * (1 - np.exp(-kappa * dt))) / (4 * kappa)\n",
    "        nc = np.exp(-kappa * dt) / c * x2[t - 1] \n",
    "        x2[t] = c * npr.noncentral_chisquare(df, nc, size=I)\n",
    "    return x2\n",
    "x2 = srd_exact()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "uuid": "98648791-2251-4313-baef-e65e4f3ea059"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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g5W3Tm4q2znletsg83Sxbt37ya7q+cpO0hrzT+HhE3FFhnKtVyr4rhgDuA66o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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8f4c358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x2[-1], bins=50)\n",
    "plt.xlabel('value')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: srd_hist_exact\n",
    "# title: Simulated square-root diffusion at maturity (exact scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "uuid": "3d998e1a-e225-4de8-b09b-abf8651d30cb"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Sfcpdc1NKbVFK/WJX9qxS6ri1fItSarSz+7dsCV6exSThi19mLrkjRoC7O3eFh7P3s71c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928/Bv8xShqjv4SBSJm4ysy+J59Y7aWngoArLizHiQhzP4lRattSW2XqClR8LbxhqAo3w579+6N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\n183/A9BBCEkqv06/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x93cc9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x2[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: srd_dt_exact\n",
    "# title: Simulated square-root diffusion paths (exact scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "uuid": "fc247695-7a20-4452-8c74-96ace26f2ebe"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min          0.004          0.005\n",
      "           max          0.048          0.050\n",
      "          mean          0.020          0.020\n",
      "           std          0.006          0.006\n",
      "          skew          0.528          0.595\n",
      "      kurtosis          0.342          0.512\n"
     ]
    }
   ],
   "source": [
    "print_statistics(x1[-1], x2[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "uuid": "7f49cc7d-5264-459c-a9b7-d602daed9f2b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1.5 s\n"
     ]
    }
   ],
   "source": [
    "I = 250000\n",
    "%time x1 = srd_euler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "uuid": "ede482c4-ec2c-43e2-8128-0c97b44469bd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.49 s, sys: 3 ms, total: 1.49 s\n",
      "Wall time: 1.49 s\n"
     ]
    }
   ],
   "source": [
    "%time x2 = srd_exact()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "uuid": "84a26be5-eede-4478-9f67-c6a97f9804f9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size     250000.000     250000.000\n",
      "           min          0.003          0.004\n",
      "           max          0.063          0.057\n",
      "          mean          0.020          0.020\n",
      "           std          0.006          0.006\n",
      "          skew          0.563          0.587\n",
      "      kurtosis          0.504          0.511\n"
     ]
    }
   ],
   "source": [
    "print_statistics(x1[-1], x2[-1])\n",
    "x1 = 0.0; x2 = 0.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stochastic Volatility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "uuid": "786bc4c9-bff7-4a6d-9ae5-1f62c1813518"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "v0 = 0.1\n",
    "kappa = 3.0\n",
    "theta = 0.25\n",
    "sigma = 0.1\n",
    "rho = 0.6\n",
    "T = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "uuid": "0db5ac22-1065-4fd5-92a8-3ccb0780d34c"
   },
   "outputs": [],
   "source": [
    "corr_mat = np.zeros((2, 2))\n",
    "corr_mat[0, :] = [1.0, rho]\n",
    "corr_mat[1, :] = [rho, 1.0]\n",
    "cho_mat = np.linalg.cholesky(corr_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "uuid": "41b7d810-38b5-4831-bb66-84a57c97415b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1. ,  0. ],\n",
       "       [ 0.6,  0.8]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cho_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "uuid": "b16ca288-23eb-463b-9b63-4765eea564f9"
   },
   "outputs": [],
   "source": [
    "M = 50\n",
    "I = 10000\n",
    "ran_num = npr.standard_normal((2, M + 1, I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "uuid": "e7ae274e-fec0-43f5-a171-0dd5f131e6c2"
   },
   "outputs": [],
   "source": [
    "dt = T / M\n",
    "v = np.zeros_like(ran_num[0])\n",
    "vh = np.zeros_like(v)\n",
    "v[0] = v0\n",
    "vh[0] = v0\n",
    "for t in range(1, M + 1):\n",
    "    ran = np.dot(cho_mat, ran_num[:, t, :])\n",
    "    vh[t] = (vh[t - 1] + kappa * (theta - np.maximum(vh[t - 1], 0)) * dt\n",
    "          + sigma * np.sqrt(np.maximum(vh[t - 1], 0)) * np.sqrt(dt)  \n",
    "          * ran[1])\n",
    "v = np.maximum(vh, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "uuid": "0016d6a1-4c5c-4617-847a-d0d1510c3fb9"
   },
   "outputs": [],
   "source": [
    "S = np.zeros_like(ran_num[0])\n",
    "S[0] = S0\n",
    "for t in range(1, M + 1):\n",
    "    ran = np.dot(cho_mat, ran_num[:, t, :])\n",
    "    S[t] = S[t - 1] * np.exp((r - 0.5 * v[t]) * dt +\n",
    "                    np.sqrt(v[t]) * ran[0] * np.sqrt(dt))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "uuid": "5db99fd6-5e32-4c1f-8186-fe6ac910b0c8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zS47vETYJrsnBNTlmk+aanG5yTU5zOU/jcTmJfsRncszMzBLnX9aOxjU5UyrV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\n7aRu+wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e978e510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 5))\n",
    "ax1.hist(S[-1], bins=50)\n",
    "ax1.set_xlabel('index level')\n",
    "ax1.set_ylabel('frequency')\n",
    "ax1.grid(True)\n",
    "ax2.hist(v[-1], bins=50)\n",
    "ax2.set_xlabel('volatility')\n",
    "ax2.grid(True)\n",
    "# tag: sv_hist\n",
    "# title: Simulated stochastic volatility model at maturity\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "uuid": "0b542695-d86d-47d9-8be4-760cd9a7786b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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m8NrlhQHXD0D8Q/Eo+7UMUyKnwNrr8tgCRkKip8TG3ov6+iRMm5bU36pcFvRaZBlBED7p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eLVYDbAqBphb2WP4JbBCPIMQlDLIHjYezTqXDk54lI6dwYCAxvOd37b5RmNGBIdjYTycvwSFIQT\npaX4NiMDp8vL4WZpiXGtWmGitzc6O9T+XeUbjYguKamVzCQ629ujs4MDOtvbo1tuLm569VVotmwB\nBg4EXnwRJj8/nGnVCoft7RFdWoqoymNzjUY83aoVFt1UGbSqvBw4fRo4dUqk9HTA2xto27YmeXvX\nK67l5cCuXUIUN20CTp6svd8SRtxmocVYq19wt/E3uKoFlTssoYZ2R0X3m1HQZQAy292MTI0v8vOB\nffvC4eIyBDk5QG6uaO+qZDIBCxYIwWkSpHh4srUFAgJq7dq8GRg1CigpAWxsAL2+ak8F3N1XwGCY\njZKSeHh5+aN79zvg4hIIW9tAaDSBMBjaITfXCjk5wJkzQvCHDRMiPbDuc2WzMJlMyM3NhYuLC+zs\n7BrMJ4VQ0mjKjeWYvGkyvov8DoPaDsJPo36Cj5NPrTyJukR8deArLIpaBF2FDj28e+C5ns9hVJdR\ncLdr2hP0pWBSTfjt5G9YdWIVdqfsRnpxOgDA2cYZN/vdjFv8hDA6WjviRM4JkXLF69mCs1CpAgCc\nrJ0w2H8whgUMw9CAoQhe8gcs3nkX2LJF9KSayc6knZixcwa2J2yHShW9fHphbNexeCz4MXg5eolM\nRiOwerUQwIMHRbdp4kRg0iQUejjBzsoOOSZi+NGjiC8rw4+dO+Phli0bXYezBWfxxf4v8H3U9yg2\nFGOA3wC80u8V3H/T/Rd8yLnSFJlMuO3IERwtKcGfISHVgq+SCNfpsDA9Hb/l5sJIYqCLCwa6uCCm\ntBTRJSVIrrkzw8faGt0dHWGpKDhZVoYz5eUwV+5TSLy+fTs++PxzOBUXVx9Tbm2NFC8v5Pn6wuDn\nB/vWrdG9tBSWVeKXklK7sg4Oort0LtbWgJ9fjTC2aSOSn1/Nq709kpKA9GQTfE7tgMf2X2C/aS2U\nvDzAyQm4/37g4YeFoO7eLZ4mDhwQagqIcgYMEPnuvVeI1nmQTegFGo1ARASwYQOwcaNQKmtrYPly\n0YU/h/x84M47hVaWlorzAOJcAQGEu3sWcnJ2Qqf7HwoLtdXHaTQaBAQEIDAwEO3b3wRVfQCrVg1A\ndraCoUOFIA4adOFqqqqKXbt2ISIiAtnZ2cjKyqr1mpeXB5JwcXHBM888g0mTJlWH2DwXKYSSJvPj\n0R/x7O/PwsHKAStHrcSwgGHYkbQDC/YvwPq49VCgYFSXUXi5z8u42e9mKJdig7kMkESiLhG7U3Yj\nIjkCEckROJ5zvFYeKwsrBLYIRBfPLtWps0dn3ORxE6w0VjUZKyqALl3EDS8qqsYE2UzSi9Pxc8zP\n+PHoj4jKjIJG0eA2v8EYm+GJbj9pkWjIRkKgJxIHdkWCrz0SS1KRUJCAQn0h7Czt0Ld1X/TyvRl/\nmX1xXOOPrzp3wwu+vvW2QXpxOmKyY3As+xh2Ju3E7/G/Q2OhwaNBj2Jy38no7dv7ovVVScSWlaHY\nbEYXe3s4XeL1X4wysxl3HT2KPUVFWBsUhJEe9fc8sw0GLMvMxLcZGThTXo5O9vbo7uiIUEdHdHd0\nRDdHR7S0rm2C16sqTpWV4eQ5KSk/H0EZGehXUICuubkIyMpCi7Q0WCQlAUlJomvl7g507ChSYGDN\n+44dAWdn0T2qyn9uSkwUr5mZNWpRhYeHEMTUVHEOR0chaI88IlSmHmGDwQAcOVIjjDt3AllZgKsr\n8Nhjwu7ct2/j1U+nE13TDRuAv/4S29bWopt2zz3C9rl7t+hWTppUbxEVFcL8e/Jk7RQXJ6p7770G\nPP74SRiNRxEfH1+dYmNjUVFRgQ4dOqJTpwnYv/9J5Ob64NZbhSAOHlz7PKdPn8YPP/yA5cuXIzEx\nEQDg7OwMLy8veHl5oWXLltWvnp6e2LVrF1avXg2SuPfeezF58mQMHjy4+t4khVByUeoz8Z3IOYGH\nVz2Mkzkn0bFFR8TnxaOFXQtM7DkRz/d6Hn4uflenso0kvzwfe1P2Qm/Wo4tnF7R3a19b8C7EmjXA\nQw8B//sf8OyzDWarr90uxIn9v2PF6g+wwhyNJJfav1M7SzsEuAUgwDUA/q7+aOvSFmnFadiVvAvR\nmdFQqUJRNKBDe/T1G4BXutyBgvKCauGLyY5BQUVBdXmtnVtjXLdxeKH3C3V69VWQRLJej4NFRThQ\nXIyDxcU4XFyMYrO5Oo+/rS2CHRzQtTIFOzigk709rBsYZ2ss4eHhuHnQINwXE4O/8/OxsnNnPObl\nddHjSMJAwuYSz98gBoMQh0stIz0dSE4WKSWl5r2Li/ht3XWXGEhrCmYzwufNw5CoKGFCLy8Xg47j\nxgFPPAG0bi3yVanViRM1SnXihFArk0mI8j33CCG+/XYhyoAo7/HHgfXrgffeA2bMaLTIFhYCc+eK\nVFYGPPmkELiqzllJSQnWrFmDxYsXY+fOnbCwsMBNN92F9PQJ0OnuQY8e1rC31yEr61dkZi5DcfEe\nAAqcnW+Hq+uT8PG5D126OKJzZ1Qnf//aFunU1FR88803WLhwIfLy8hASEoKXX34Zo0ePhr29/fUn\nhIqiuAJYBCAIwkPsKQCnIFarbwsgEcAjJHXnHSeFsBk0dEMvNZTi9c2v41j2MUwInYDRXUfDzqqJ\nf97rERIYMkTcPGbMAAoKhH2o6rXyfXh+Pob07Sueyvv0AXr2rLmpnFvWli3C/LlpE2BjA3XMaOwd\nOxipnrbwd/VHgFsAPO09G+xZF+mLsC91H3Yk7sTiuM3IzDsCqCLSvrONM7q27IrglsHVr8Etg9HC\nvkW9ZWXo9ViTk4NN+fk4WFyMbKMRAGCtKOjm6IjeTk7o7eQENysrxJSWIqa0FMdKShBXXg5T5X/L\nUlEwxNUVk319MaJFC1g0wyKwbft2fNOyJdbk5uK7wEA841O/WEtqU/1fLSoCVq0Cli0TA5GKIn6D\neXnA2bPCUQgQStGunVCOkBAhwP36AZoGxtFNJuCFF4DvvgMmTAAWLmySVSQnR/gkffWVqMJzzwHv\nvgu0alWT59SpU1i6dCmWLl2K9PR0ODh4wNq6D3S6bSD1sLfvDB+fcfD1HQt7e19oNOJyT54U5Vdh\nayueAzp3Bh54oMaiW15ejpUrV+Lzzz/HsWPH0KJFiyoT6nUnhMsA7CC5WFEUSwAOAN4DkEtytqIo\nbwFwI/n2ecdJIZRcHiIjhcCZTGLb1laYzNzcxKu7u7iZREeLGw8gbjpBQeKG1Lev8Oj84gshqF5e\nwIsvih5mE8b5zock3jodh09jd8Le1h23egXiDnd33O7mhpvs7esV07RK8VuVk4PdhYUggEA7O9zs\n4lItfCGOjhfsZRlUFXFlZdVjcyuyspBmMCDQzg6TW7fGuFat4NDQzfU8VBITYmOxLCsL89q3xyt+\n17Z14Zrn7Fnghx+EZ0vr1kIZunSp8Viqz+x6IUjRnZsxAxg5Evj5Z8C+IS/W+klNFYd//71wsnnx\nRaBHD9EhdnUVydHRjEOHtmLlyu9x8OBB3H77Ixgy5Ek42ASi6PBpKEei4XjmCFpmHkEJHbGi93xY\nB/jC1laIbHGxsEKfPAmkpYmO8Zdf1jyLkkR4eDg+//xzrF+//voSQkVRXABEkWx33uexAAaTzFIU\npRWAcNazHuHVrr/kX0RGhrgpuLld2IyVkyOcXfbvFw4OBw6IXiMAhIYCr74q/M9tbC5b1Tbl5WF9\nXh625OfjTEUFAMDX2hq3ubnhdnd3hDo6YmtBAVZlZ2N3UREAINjBAQ97euIhT090cbg0r16jqmJ1\nTg7mpabiYHExXC0tMdHbG5N8feFXz41XJZFjNCJNr8e36elYmJGBaf7++KAexwbJNcI33wgF699f\nONQ0cToJIPyNwsLE8GNDt+YWGh3GWqxEkDEKoYhGMGJgB/GbNsAKKU5d4FN2GuWKPSZYr8D6sttr\nHe/mJnQ6LU08Y86cKXyKqoebCwuhuLped0IYCmAhxCr13QAcBvAKgFSSbpV5FIgV6t3OO1YKYTNo\n6liXRNBgu5HCC6+oCOje/dImdDWChPJybC0owJaCAmwrKEB+VS8WQNdK8XvY0xM3XaL41QdJ7C0q\nwvzUVKzJyYECYJSnJ7ytrZFmMCBNr0eaXo8MgwHGc/6bj6Sl4efRo6+6o9X1xhX/r65eDYwZA3To\nIN537tysYqqmepw7f7KwEGixZyPuWPssnEsyUG7fAsXtukENCYV9/25wuqUblC6dxZjtyZPCq/bE\nCZS/8T5OPvwBEpI1SEgQHeLYWODwYfGXq8LfqxzvOn+J0Smz4FiR3yQhvBZ8qi0B9AAwieRBRVHm\nQyzEWw3JqgC2Esm1h6KIG8cVIsDODv+xs8N/fHxgJhFVXIzokhIMdHVFpyaatJqKoii42cUFN7u4\nIKmiAl+mpWFRRgZMJHytreFrY4PBrq7wtbGp3m5nZ4d8Uorg9cBDD4mu1X33CXOrvz8wdKhIt94q\nZso3Ag+Pc3pogFDGyZOBlSvF2OV362DXuzfsGvpNdO4sLC6TJsHu0+nocTgCPVasAEbVDD6SQEwM\n8Mw4I0KjFmNa7nS0ykrH3xbDAWxq0mVfCz3CVgD2kgyo3L4FwDsA2gG4lWSmoijeALT1mUbHjRtX\nPY/E1dUVoaGh1U9Q4eHhACC35bbc/ge3q9zWr5X6yO3LsJ2SgvA5c4CoKAyJiRHOYgDg54chI0cC\nQ4ci3NIScHG5eHm5ucCLLyI8Lw944gkMWbgQsLZufH0SEsTxtrbA++9jyKuviv3btwNaLQb//DN2\nnD6N2fDESdseGDq6HxYvnnZ9mUYBQFGUnQCeIRmvKEoYgKrH2jySnyiK8jbECvXSWUYikUiuJGYz\ncPQosG0bsH27mN9YWiosISEhNb3FQYOEd0wVWVlizHHNGuFhvWSJCBfYHGJiRG/11Clg2jQxFv/e\ne6JeISHAzJnY43Y3HntcQWYmYDQ2bR7hVQ+cXSlk3QAcBHAEwFoALgDcAWwFEA9gM4QQyqDbl4Gr\ntR7h9Y5st+Yj2655XJPtZjCIqNszZpBDh4oI4gBpYUH27i1WSJk/X6zuYmMjVj5uZEDzC1JcLCKC\nV0U6b9+eXLFCLOlSSV6eWKQFTQy6fS2MEYLkEQD1hcFofswriUQikVx+rKxE+LcBA4D//ldM6N+3\nT0Qd375dzKE1GsX8xcWLm+1wUwdHR+DHH8XcSL1ezOK3qh00w90dWLeuwTjrDXJNmEabizSNSiQS\nyTVGaakwYXbt2vBE/n8YGWJNIpFIJDc0TRXCfyiAn+RapsobS9I0ZLs1H9l2zUO225VBCqFEIpFI\nbmikaVQikUgk/yqkaVQikUgkkiYghfAGRI47NA/Zbs1Htl3zkO12ZZBCKJFIJJIbGjlGKJFIJJJ/\nFXKMUCKRSCSSJnDNCKGiKBpFUaIURdlYue2uKMoWRVHiFUXZrCiK69Wu478FOe7QPGS7NR/Zds1D\nttuV4ZoRQgCTIRbnrbJ1vg1gC8lAANtw3hqFkuYTHR19tatwXSLbrfnItmsest2uDNeEECqK0hrA\nCACLAFTZde8FsKzy/TIA91+Fqv0r0el0V7sK1yWy3ZqPbLvmIdvtynBNCCGAeQCmAFDP+cyLZFbl\n+ywAXle8VhKJRCL513PVhVBRlHsAZJOMQk1vsBaVrqHSPfQykZiYeLWrcF0i2635yLZrHrLdrgxX\nffqEoigfAXgCgAmALQBniMV5ewMYQjJTURRvAFqSN513rBRHiUQikdThul2GSVGUwQDeIDlSUZTZ\nAPJIfqIoytsQK9RLhxmJRCKRXFauumm0HqqUeRaA2xVFiQcwtHJbIpFIJJLLyjXVI5RIJBKJ5Epz\nLfYIJRKJRCK5YkghlEgkEskNjRRCiUQikdzQSCGUSCQSyQ2NFEKJRCKR3NBIIZRIJBLJDY0UQolE\nIpHc0EghlEgkEskNjRRCiUQikdzQSCGUSCQSyQ2NFEKJRCKR3NBIIZRIJBLJDY0UQolEIpHc0Egh\nlEgkEskNjRRCiUQikdzQSCGUSCQSyQ2NFEKJRCKR3NBIIZRIJBLJDY0UQolEIvsyHKkAACAASURB\nVJHc0EghlEgkEskNjRRCiUQikdzQSCGUSCQSyQ2NFEKJRCKR3NBIIZRIJBLJDY0UQolEIpHc0Egh\nlEgkEskNjRRCiUQikdzQWF7tClwKiqLwatdBIpFIJNceJJXG5r3ue4QkZWpimjp16lWvw/WYZLvJ\ntpPtdn2kpnLdC6FEIpFIJJeCFMIbkMTExKtdhesS2W7NR7Zd85DtdmWQQngDEhoaerWrcF0i2635\nyLZrHrLdrgxKc+yp1wqKovB6rr9EIpFILj+KooA3krOMRCKRSCSXghTCG5Dw8PCrXYXrEtluzUe2\nXfOQ7XZlkEIokUgkkhsaOUYokUgkkn8VcoxQIpFIJBdFdiJqkEJ4AyLHHZqHbLfmI9uuefwT7WY0\n5uPYsZE4dCgEZWWnLnv51yNSCCUSieQGoaTkKA4f7o38/L+h16chMrIfdLodV7taVx05RiiRSCT/\nMvSqipSKCnSwt6/+LDv7F8TGToClpQuCgtbA2roljh27B+XlZxAY+C28vcdfvQpfZpo6RiiFUCKR\nSJrIwaIizElJwYHiYtxkb48QBweEODoixMEBneztYW1x9Yxth4qKMC42FifKyvBa69aYGdAGaYn/\nRUrKp3B2HoCgoFWwsfEGABiNOhw//hB0um1o0+ZtBATMhKJcZUPhDz8AUVHAzJnAOULeFKQQSi5K\neHg4hgwZcrWrcd0h2635/BvaTiXxR14e5qSkYGdhIVw0Gtzm5obT5eU4WVYGQ+W9yEpRqsWxu5MT\n+js7o4ejI2w1miafsyntpldVzEhMxKzkZHhZW2Oomxs2ZMVjtuYjdDIfgI/P8+jQYT4sLKxrX5dq\nxKlTk5CR8S08PEahc+cfoNE0T4AuCb0emDwZWLhQbPfsCaxfD/j6VmchiTfPnoVRVTGnfXtYNvDA\n0VQhvK7XI5RIJJJ/mgqzGcuzsvBZSgriysvRxsYG89q3x9Pe3nCyFLdQo6oivrwcR0tKcLS0FMdK\nSrCjsBArsrMBANaKgh6Votjf2Rn9razQ+tAhoE0boFMnGFUVuUYjso1G5BgMyDYakW80giUlGEhC\no1z4nh5ZXIzxsbE4VlqK8a1aYV779rDUn8BT+ZNhNqbjc+VNjHR6BR0VqzrHWlhYITDwf7C374Qz\nZ95AdHQSgoM3VPcarwjp6cBDD4H79yL9yzugb++EgEc3QendG9iwAejVCwCwJDMTc1JSAABZRiN+\nuOkmWF2G3rfsEUokEkk96FUVnyYn44u0NGQbjeju6Igpfn542NOzwZ7I+WQZDNhbWChSRgYOGo2o\nqDy2dXY2HMvLkd2yJfLt7Bosw8vKCvd6eOB+Dw8Mc3ODzTnnNqgqZiYl4aPkZHhaWeHbwEDc4+EB\nnW4Xjh69E5aW7vAK/An/SXWCVqfDo56e+F9gIFyt6goiAOTmbsCJE6NhZeWG4OB1cHLq2YQWq6qU\nAVi2DLj5ZiAo6OL59+wBRo1CcUsd4uf4oNjqLACgte2T6PDYDiA7G1i2DCdGjECvw4fR39kZd7i7\n4+2zZ/Gghwd+6tKljilamkYlEomksZSVNTgO9WJ8PL5OT8dd7u54w88Pt7q6QrlIz6wWRUXCtLd5\ns0jZ2TBYWuLI8OHYO3w49t10E0z5+WgZGQnP9HS0tLNDy8GD0XLoUHg6OsLJ0hK7dDr8lpuLP/Pz\nUWI2w1GjwQh3d9zv4YG2trZ4IT4eR0pLMdbLC5936AD3SoGLjLwFen0KevTYDxubVjCTmJ2cjPcT\nEtDaxgYru3TBzS4u9Va7uDgKMTH3Qq/PQOvWk+HvPw2Wlo6Nu2YSeOYZYPFisd2nDzBhAvDYY8D5\n5yOBhQthevslJLzkgLRhxbC2bon27eeisHA30tO/QqD3p/CZ8BvKDx1Cn7VrkeXqiiO9esHbxgaf\np6bildOnMbJFC6wKCqr1gNBUIbzqKwlf4irElDQdrVZ7tatwXSLbrfk0q+2Skshx48iuXcnnniN/\n+YXMyrq0iqgqefQoOWMG2bs3CZDffFMn28acHEKr5WunTjX/PAMGiPI9PcnRo8lly8j09Lp5KyrE\nvtBQkd/Dg/zvf8n09Op2qzCb+WduLv8TG8uWERGEVktotfSKiOC6nJxaxel0EdRqwZSUBXVOtVen\nY8DevdRotXzl1Clq8/NZYTbXyWcw5DM29llqteCePa2Znb2Wqqpe/LrnzWOJrS21H33E8nnzyOBg\ncU22tuSYMeS2baTZTJaXU316ArNuBXdvtKFWqzA+fhKNRh1J0mw28siRu6jVapiXsZETv/mG0Gr5\n15QpZFlZ9em+Tk0ltFreGR3NMpOpsulNrNSGxmtJUzI3NQEYDiAWwCkAb9WzfwyAIwCOAtgNIOSc\nfYmVn0cBONBA+Rf/YiR1kDf05iHbrfk0qe0KC8l33hE3TxsbcuhQ0slJ3K4AIYyTJ5Pr1pEFBRcv\nz2Agt28XxwQE1JTTty/Zowdpb0+ePl2dPVOvp2dEBEMOHKhXJBrFzz+Lc3zxhbjxNwZVJbVa8r77\nSEUhrayo7dOH/PprMjm5OptJVblbp+OXqanMNRjqFHP06H3ctasFTaaSek+jMxr55IkT1FSKqd2O\nHbwjOpqzk5J4uKiI5nMET6fbwwMHQqjVgkeP3sPy8sQGqq5y96ZNfHrKFDr+/Teh1bL93r38MyeH\nPHiQfP550sVFtIm/P0uHdWL0bFCrBQ8e7MnCwoN1yjQai3jgQAi37XCiv3Yx31yxQhzfp0+t9liU\nnk5Fq+XQqCjmFp/k4cMDmiyE/5hpVFEUDYA4ALcBSANwEMDjJE+ek6c/gBMkCxVFGQ4gjGS/yn0J\nAHqSzL/AOfhP1V8ikVxhjEbgu++AsDAgJwd44gngww+FQ4nJBBw+DGzfLtLu3UB5OWBhAXh7AzY2\nNcnauuZVowEOHgQKCsRnt90G3HcfcM894rjUVCA4GAgJAcLDQUXB3ceOQavT4VDPnghycGj6dVRU\nAJ07C1Pg4cOiDk3l9Gngf/8D1q0DzpwRn4WGinqPHCmcR+oZpywtPYmDB7ugbdupCAgIu+Apikwm\n7NDpsLWgANsKCnC8rAwA0MLSEre6uaGvkxM62dujo501bPO+RXJiGADC338qWrd+FRYWVkjX67E8\nKwtLkpIQZzbDQa/HIz4+GOThgVnJyYgrL8f9Hh6Y36ED2pIwrF+GlIRZSO2ZBAtLe7TrNBs+Ps9B\nyEVd4nWnEBPdH4pijTv6HobDX/uAsWOFSTskBBg6FBg6FMuDumB98nxMxCLYaWwxaJDu2hgjrBS5\nqSSHV26/DQAkZzWQ3w3AMZKtK7cTAPQimXeBc0ghlEiud0jhGfjmm0B8PDBkCDBnjnCfbwi9Hti/\nH9BqgeRksW0w1H01GIAuXYT43XEHUJ+wLV0KPPUUMH8+vhw1Ci+dPo0vOnTApNat661qXh5w9qzQ\nJ0tL4IEHxGs1n34qrmXrVmDYsEtvm7g4YONG4PffgYgIQFUBLy9xPS1bAnZ2YpzTzg6x/quQ7XwI\n/fK/hnWbrmKMrpFk6PXYVlCAbZXimKrXV+/TAOhlU4in1c/R0ahFuVUgtllPwDelISiDHW45dQoT\ntm7Fw7NmwTEgAIBw5JmbkoIZSUmwZzHmufyNNsVLoJrL4OU1Fu3azbqgZ6pBVXFLVBTMZdGYy5fh\n6BCM0NBwaM6mAqtWVT8QlbtWIPYtoDAU2M++2M7XsHnYo9fGGCGAhwB8d872WABfXCD/GwC+PWf7\nLIRZ9BCA/zRwTL3ddMmFkSa+5iHbrfk02HZnzpCDBwuT1003kRs3ChPhlURVybvvZkynTrTVajni\nyBGqqsrMTPLbb8kpU8hRo8QQnrNzjWW1KnXqRK5dW1ntnBxhArz77stStTrtlpdH/vgj+dhjZKtW\npIODMKMCrGgBhm8G414+p3KTJpF6fbPOnWcwcF9hIX/IyOB7Z87w4ZgYdjtwgEPCP+IKrTe1WnBr\nuB33fevHnEEamndtr1OG0VjM6NPT+Fe4E7Va8NOdw7glbU+jzv/6qVOEVsvV2dnMzv6NWq3CmJiH\nqKrC1KyqKlMTF3CH1pY7t9gw/aUOXD1kMC23bGmyafSfnEfY6K6aoii3ApgAYMA5Hw8gmaEoiieA\nLYqixJLcdbkrKZHc8Pz0E/DXX6JXNGQI0BTPyEshLk70mMrKgG++Ed6GlldharOiQP+//2H0li1w\nKinBc0pfjB2rYNUqYa21sQECAoB27YBbbgHatxfv27cXFsx33gEefBDo3x9Y7T0NPiUlwOzZ/0xd\n3d2BMWNEqoIEDAaknpkCZn8Fvxe2Af/xAJYsAebOFabhX38VJuamnMrKCn2trNDX2bnW5yp7IVP/\nCmzK9iNv3UvIbhmDmGmAJR6ER+yDaNnyMTg790dGxrdITv4YRmMufFuMRJrb6/hfqg3OxFfg3rxj\nGObmhq4ODujq4AAP69qT/P/My8Nnqal43scHozw9AdyP9u0/xZkzbyAh4T34+DyPuLinUVCwFW5u\nt6NTp0Wwva0NRpWU4K/du3F7E5v1n/zVpQHwO2fbD0Dq+ZkURQkB8B2A4SQLqj4nmVH5mqMoym8A\n+gCoI4Tjx4+Hv78/AMDV1RWhoaHVkRiqIrfLbbl9ObarPrtW6nNZtouKMOSFFwCdDuHLlwN+fhjy\n+uvAuHEIj46+bOcbMmRI7f0xMQgfNAggMWTXLiA4+Kq2x5TiChwtLMRHn34K7cln8Lvzaxg5Mhz3\n3AOMGzcEFhb1H+/iAhw9OgRLlwILpvyAE3u/xpG2E9EWXZB9mepXxYXymzQV+GPrIjg7D67ZP3Ik\n4OKCIXPmAD16IPzNN4E+fS58PpMJQ9LTgXnzEJ6XB3TrhiGPPw4MHozwU6eq8/vY2iH83Q3AvBgM\neuMVFLx9J37/fR4iI39CSMhiABaIjlbh6NgTjzzyO5yd+yIvPBxfm0uxr317LEhNxYZt28SFhYbC\ny8oKvidPop2dHW4bMgTvJSSgXWws7jebgcBAAMDp0z2QkjISwCykpi5AVJQKX99XMXjwZ9ixYweW\nLv0AAKr1oEk0pfvYlAQhsmcA+AOwBhANoPN5edoAOA2g33mf2wNwqnzvAOFRekc952hUF1sikTTA\nlCnCtHbgALl0qfCkBEg7O/Lpp8lDhy7/OSMjyRYtSB8f8uTJSypq1fFV/PnYzw3u372bXLJEOHGu\nX09u3kzu2iUcGWNiRFUenJknpiNMjuM25/totLJl6eGm18t4972ssHFiO8csWliI5ktLu4SLawJJ\nSZ9QqwWLiiKrP6ueZRAfLzxtFYWcOpWsnGZQi5IS8vPPST8/8f2HhAjz7rm24A4dxEX98AO5ejVp\naUnedVet8kymMmZnr2Z8/MssKAhvsL6qqjK9ooKbcnP57vEIDtn8OVv9+BQtFvQhZrpS+cSXe3KS\n6hxnNhsYE/MQo6PvZFnZ2QbLxzU2feIuCM/R0wDeqfzsWQDPVr5fBCAPYiywepoEgHaVwhkNIKbq\n2HrKb7AhJA0jx7qax7+u3ZKTxfSEJ5+s/XlkJPmf/4hpBYCYbzdzprj5HT1aax5XY6luu/37SVdX\nsk2bWlMWmsNvJ3+jEqYQYeBHOz+qM89t8+bq4bOGk7OBWL2bzmv2c/MOE9X0DNLdXTwQ1CcYDV+g\nKPCjj5iTQ77yCmllJYbxmjsVURSrvWges7mCu3d7Mzr6dpJirPLFF8X5x40jjx0jWVoqvmeAvOMO\nMZZJijHHadPEgwlADhxI/vFHzTitySQehj77jLz3XvHdVTVe586kTtfka8ouyebbW97msGXD6DbL\njQgDEQZaTrdkt2+68f5fH6f1DGuOWDGCZrV501euKSH8p5MUwubxr7uhXyGuWrvp9eS8eeKJffNm\nMjX18jiUTJhAWluTiYn179fpyAULyKCgugrSpg15223kCy+Q8+eThw9fsE5arVZ0xZycyPbtGz5n\nIzmQeoB2H9qxz3d9OHrNaCIMfHPzm9VimJQk7u1BQWRcHHn8uLif79olmnD9enLlzyp7/XmMVtpw\nRhUV1RS+cqW4xk8+aVxlzGYxH7FNm1oPCceOiTr4+4uvrDk05jeXnr6IWi2Yl7eFqkq+8Yao/tCh\nNc8yI0aQ4VqV6sJvxcNP69ZCLR0cRIZ77iEjIi5eIZOJjIoSQQjOmcvXWAwmAwcuHkjL6Zbs9W0v\nTtwwkQsPLeTBtIMsN5aTJPPK8vjWlreIMPDjXR83+RykFEKJ5N9Fbi45aFBdIXJ2Fr2W8ePJ2bPF\n5PItW0TPJCJC9LwiI0UP7uTJmh5AFcePkxYW5KuvNq4eRUVC7H76SfQgxowRPcWqSdKAuLk+/zz5\n118iWsq5bNsm7sqdOjVfFSpJKEig16de9J/vz8ziTJpVM1/4/QUiDJy4YSJLy0zs00doblxc/WWU\nmkx8KCaG0Go55/wbuqqSDz4oHhKOH794hX74QVz/jz/W2XXgAOnoSHbpIr7Ky42qmrlvXycePNid\nqqpy2jRRlRdfFJeRm0tOny6C21R17rfMOkTV35/UaMixY8Vv5Arxxt9vEGHgiqMr6t1fWFHI4K+D\niTDQY7YHLaZZUHtW2+TzSCGUSK4CSUmfct++DszN/fPyFRobK8ZlbGxELyUzU0RI+eorcacbOlTY\n3i5o+6tMlpbk668LQSNF9BJn57oC2VRUVYQNW7KEfOCBmh6Gg4MQk6VLyV9/FVFigoPFNVwCBeUF\n7PJVF7rOcuWJ7BPnVEPlu1vfJcLAjm8/RlgYuGZN/WWklJezx8GDVCpFsN7QYVlZItRZz56iB9RQ\nb7e0VDwA9OrVYAQZrVZ8hb171zT/5SInZx21WjAz8yd+9plo+vHj61alrEx04jp0EHm6BhRz7Vf1\nhHv7B1l7Yi0RBr7w+wv17jeajbxz+Z20nG7Jt7a8Rb+5ftUm028OfkOTWZiqC/cVMn9r/gVDvkkh\nlFwUaRptHg21W17e39RqFe7Y4UCtFoyNfZZGY/GlnWz7djEe4+kpPD4uRH6+6Hrs3CmO+/tv8vff\nyd9+I1etEiL6zDPi7+7jw+puw8yZDRZpNlcwL28T4+Je5N697RgZOYgFBTsuXu/ycvLPP0VsUB+f\naiHWduhwyaKrN+k5bNkwWk234vazdeeskeRjX8wmwsB2/72bZYa6Y5n7CgvZavduOu3cyT8u1kVb\ns0b0mqra7emnxWeFhTV5PvxQ7N+584JFbdggirr1VtFEjeVi/9XDh2/m3r0BXLjQSIB8+GHSaGw4\nv8kkhnp79BDVbuhh4XITnxtP54+d2ee7PqwwVtTZr6oqn934LBEGfnf4O5LCjPrhjg+rx4Hbf96e\nizct5k7nndRCy+jbo1l8pO7/zGCQQihpBFIIm0d97VZensRdu1rwwIGuNBjyePr0FGq1CvfubUed\nrhFjLvXx/feiB9elC3m2Yc+4JrNvH9m9u/jbW1sL0+k56PXZTE9fwmPHHuTOnY7UasEdO+x45Mjd\n3L3bh1oteOTI8FqeiRdEVYU59fvvqd248ZKqrqoqn1r3FBEGLo1aSpI0qyo/S07mS/Hx3K3T8ehR\nlfb2ZMfHvqUSpnDQkkEsrKgRrR8zM2kTHs52e/cypqT+OJx1yMgQvd2HH64xA1takkOGkB99JOye\nDzzQqKKWLxeH33uvuFlfDJPpwv/VgoJd1GrBtWu/pKIIJ8/Gzp0vKxOWdXv7Oj+Dy06poZQh34TQ\n/RN3JhYk1ptnzu45RBj41pa36uxbFLmICAO953jzg6APuEGzhZ8+sJ0zHU5wkhLPp7rm8aF7TezX\nj/T1rXKQapoQymWYJJJmoqp6REUNQllZLHr2PAR7+44AAJ1uF2Jjx6GiIglt2rwJf/8wWFjYNKZA\nMTt79mwRPuvXX+suXXOprFsnYoLZ2QEmE9TXJiPzaR9kFq9CUdE+AIS1tQ9atBgJD4+RcHUdCo3G\nDmZzOdLSvkRy8scwmQrg6fkoAgJmVF/zP83MnTPxX+1/8cGgDzDt1mnQqyomxMZiZXY2rBQFRhJW\n2baw3umFzVO8kFK8EWN/G4tuXt2w4fGN+DKnHB8nJ2OwiwtWBwXVmcDdKIxGYN8+4M8/RTp6FLCy\nAo4fBzrWbYeI5Aisi12HEkNJdYo9W4K4hBK4eJbAzasUg9oOwqxhs+Dt5A0SOHYM2LRJxDeIiAD8\n/YE77xTp1lsBx3NWQzp27F7k5OzFyJFJ6NvXHn/8Ib7WxpKZKSKwqSpw4ADg49P0JmkME9ZPwNLo\npfhj9B+4q+Nddfb/dvI3jPp1FEZ1GYVfHvoFFkrdGKoT1k/AkugleOvHufg240kUlLao3mcNM7wU\nPdoEKOg4wAZtAiwwfbpcj1AiuSLEx7+I9PSvERS0Fp6eD9TaZzIV48yZ15GR8R0cHELQufNyODqG\nNFxYaakIMv3bb8DzzwMLFlz+KCtmswhUbDJBv+lnGN4YD6e1R1HhBaS80w5W9z2JFi1GwtGxe4Pr\n7hmNOqSkzEFq6jyoqh7e3k/D3/8D2Nj4Xt66nsNPx37C6LWjMabrGCx/YDkKTSY8ePw4tDodPg4I\nwAs+vhgalovDLTKh9NCBAPo5O6Nz6WEs1T4HKJag9z0Y3eMlLAkdVGcR12aTmgoUF4sA2+cRkRyB\n2364DQDgausKR2vH6pSV4ojTJxzRob0GyfbroKENuuZNQ8rqSchIE+sJBg6KRsGgp2CfOxDZv05F\neX4LWFkBAwYIURw6dCPKyu7FsmXTEBf3ATZvri2SjeXIEVFm587Ajh0NLs3YbL6P/B7PbHwG7w96\nH9NvnV5n/8G0gxi8dDBCvEKgHaeFnVX9Sl6sK0bQBz2QalcAp5WRGDR2D37Pn41+Qb74dfA3KJyu\nQ+7aXNi0tkHARwHwftK7SUJ41c2bl5IgTaPNQppGm8e57ZaRsZxaLXj69JQLHpOTs5EREV4MD7di\nUtIsqup5c9NUVczbCgoSNp358/+5WJuLF7PEHzz5160MD7emVqvwzLKBNHVpT9XCQgxkNRK9PpPx\n8S8xPNyKO3bYMjOzrsfkuTT3N7cneQ+tZ1hz0JJBrDBWMLm8nMEHDtAqPJzLMzJIknPmCJPjnDlk\nakUFZyclMfjAfjFJ/o9lxDd30mKahpbTLTl+3XiezBGT5fPz8/nCCy9w3759zapbQxzPPk63WW4M\n/CKQOaV1x0VVlXztNVFntIgnxtxFhIHObwfxza/CuXzfn3T8yJEtPmlBZbxCt1lufH7ZPL7+pp6h\noWaOHTuD27YpXLiwO/v1K2jUSlQXYv168dN75JHGrxhVWlrXMfh8ItMjaTPDhrf/cHu1o8u5JBYk\nVnv/ZpVceJ3JjeOS6dTiKJV3HdltQX8aTAauOLqCth/ass28NozKiGLBzgIe6nWIWmjlGKHk4kgh\nbB5V7VZcfJQ7dtgxMnIQzeYLeCZUotfn8NixUdRqwcjIwSwvr4yYsXt3zdSIdu2Ek0kzUFWVhYUH\nWFCwgzrdHhYWHmRxcTRLSo6ztPQUy8sTmZexkUfm21SP+8XFvcDS0nhWXpDwerSzI/c0LiByFWVl\nZxkZOYjh4dYsLNzfYL6GfnNGs5mHiopoaOAO3G9RP7aZ14Z5ZXk8WlxM30pHl635+STJHTuEE8qo\nUbWfH1756xXi03a8c+ePdPlmEEO/CeVLf75Euw/tqIQpvH/l/ewxsgcB0MbGhitXrmzSdTdEamEq\n/eb6sdWcVjyb3/D4rqoKP5v33iN37VK5JmYd285rS4SBSpjC4K+CmVaUxu/XfM/bf7idCAODv2zP\nzXv7U6sFf/99LMPCypidfVmqzdmzxc/wgw8unC8tjXz5ZeEFCwjH2m7dxDzF//yHDAsjv/uO/HVD\nAVvPbkfvT32ZWVS3krpyHYO+CqLLxy48nn3hKSrbfiilIwxs5WDg3M0/E2HgHcvv4PeR33Nj7Ea2\nntuadh/a8ZeYX6iaVWb+mCnHCCWSfxKTqQiHD/eC2VyMnj0jL7iMzLmQRFbWcpw6NQn2CUTQykDY\n/h0pltP54AMRcLqhcSsSiIoSkZ5dXc/bpeLUqUlIT//monWwygd83Z6C7y2fwsqqZozFqKpQsrNh\nOXAgkJ8vBqfqMfc1hNGYh8OHe0FVjejV6zCsrb0afeyzcXH4NiMDbpaWuKdFC9zv4YE73d3hoNFg\nT8oeDFg8AF/c9QW6dByDB2Ji4KjR4M+QEHRzdER+PtC1qzAJHjwIVMWGXha9DOPXj8fkvpMxf/h8\nrDi6AmN/G4sv7/oSjwQ9gs/3fY7ZO2bDqDGio2VHFKUUISs3C52CO8G/gz/0Zj0qTBXQm/SwsbTB\n+4Pex4iOIy56LYUVhRi4ZCASdAnYOX4nunt3b3Q7qFTx5uY38dm+z2ChWMDeyh5TB0/FK/1egUbR\nYFPs9yhIehFeNgZs03XAI/1WIdQ7tNHlXwwSePppEad75Urg8cdr709PBz75BFi4UFjYn3hCBCJP\nS6udsrMB2OUD948HOvwFLNkJy8z+8PYWyz/6+AAtvY3Y3upuJFCLpbdvwuh+w+pbWhEAsG0LMXK4\nCncYoD1siY6hVvh418eYv38+skuzAQABrgEoM5YhqzQLr/Z7FXPumAONhQaUY4QSyeWHJI4ffwi5\nuesRGrodrq6DmlZAUhJM/30dmhVrYLYH8p8Ogdu0P2HleoHxtcOHgddeA3buFHf8iROBV18FWrcG\naUZc3H+QmbkErVu/Anf3u0Eaq5OqVr4vLoDmlXfRQrkZmt83V1/LvqIi/JiVhV+ys0EAP1hb4+6R\nIwFbW2DPHsC38eN+xcXRiIq6GU5OvdCt21ZYWJwj6mZzvYvTfp+RgWfi4vCklxDOjXl5KDCZYGth\ngTvc3JAW+TbOZO7FZ2MO4bkzKehoZ4e/QkLQxtYWgLhZr14tliXs0UOUuT91PwYvHYwBbQbg77F/\nw9LCEiQxfMVw7E3ZixMvnsDXs77Gx3M/xvD3huOM6xnoTXro8nQoyiuCikcEKwAAIABJREFUm7Mb\nugR2gb21PWwtbRGXF4f4vHiMDRmLeXfOg4e9R73XrzfpMXzFcEQkR+DP0X/i9va3w2A2wGg2wsH6\nwov7Vpgq8NT6p/BzzM94tuezeLXfq3h98+v449QfmNR7EsL63o2TJx8HoMEpzeN4Y9dKFJQXYEL3\nCZhx6wx4OzXuYayKMmMZ5u6di7i8ONzZ/k6M6DgC7nbuMBiAQYOAyEjguefEMo4dOwr/qu++E1/j\nuHHAu++KZ7JzOZN/BhviNmB97AZEpOyCmWY85f05ehheRnq6ENKMDCDeGI6UoJdh9jgGrP8eiJoA\nR0fxQFOVQkKA7t3FT37U/YS3qQzrvyhDyCTP6vORREx2DLYlbMO2hG3YkbgDxYZiAICzjTOK3ilq\nkhBedfPmpSRI02izkKbR5vHLL89RqwWTk+c07cDUVGFPsrYmbWyovvYqkyLfoVar4Z49fszP19Y9\nJiWlJjakp6cYABszRtgBLS1pHv8Ej++5m1otePbs1LqTi3U64a//wAPC5GlhQUZF8VRpKaeePcv2\ne/cSWi1td+zgY8ePs/ehQ4RWy7dXraLq6CiCNDdx8CkzcyW1WjA+flLNh+vWkfb21I4cWWv+3cHC\nQtqEh/O26GiaKutuMJu5LT+fL8XHs9XWX4kwhVg8htBqOTgykvnnzDmoioL24Yc1p0ovSqfPZz4M\nmB/A3NLacwTP5J+h3Yd27PZMNwLgxIkTa7WZqqqcM2cOFUVhz549mVoZ/abCWMEPtn9Ay+mW9Jzt\nyZ+O/VSnrc2qmY+uepQIA3888iPP5p/llM1T6P6JOzXTNOz7XV++s/Udbj69maWG0lrH5pbm8pbF\ntxBh4CcRn9Qq++W/XibGgR+vBg8c6MaysgSSZH5ZPl/b9BqtplvRYaYDp4VPY4n+4tNBVFXlquOr\n2GZeG2Iq6DKlJ/HwKGLQh3TvtpsunkUNxmPw8yOnTFG5cUsBd585zLUn1nL18dV8e8vb7PJVl+p4\noV2/7sr3tr3Hg2kHa507SZfER1Y9QoSBbee15YrDa7l3r1jvcdIksSSlu3vN+RwdSY1GZSeLImoH\nH7vg5HlSzDncnbSbd6+4W9RFjhFKLoYUwqaTlbWK8+ZZ8NixBy/6p6wmMVFMLLe2FnPPnn66VnzG\nwsL93LevI7VahadPv0mzuUKM133wgRAva2vyrbdqBzZOTKR58os89qGGWi2YOP0mMZlbVcnsbHLR\nIrEigJWV+Ht7e7P8pZf4VUQE+x0+TGi1VLRaDo2K4pL0dBZWzr42ms2ckZBAy/BwPjpvHs1WVuLu\n1JTZ3yRPnXqdWi2Ynr6E3LpVXEPbttQqirib/vEHs/V6+u3ZwzZ79jCngYlvL/zxAq1mWHNyzD6+\nf/YsK84ZQ0xJEbEG+vWrmTxeYaxgv0X9aD/Tnkcyj9Rb5vhPxhMK2GNQDxobmHW+YcMGOjo60sfH\nh4fOWXnjaOZR9v62NxEGjlw5kimFKdX7Xt30KhEGPr3+ad6z8h4qYQo10zQc9csovrv1Xd78/c20\nnG5JhIFW0604aMkgTtVO5frY9Qz8IpA2M2zqrKBhNBbz8JEH6f0c2OJjG6bp6o43nso7xVG/jCLC\nQJ/PfLg4cnG9TikkeSzrGIcuG0qEgZ2mD2dwT1216CgWJtr6xhEhy4g7XmXLZ5+g1R3/pdLrG3rf\ntZTeA/+idavTIr9VKdF/DjHFUwjOVAt2/DyQ08On1zsmWmYo4/Tw6bT70I52H9pxevj0egMdkOIn\nfOqUiPoGkG1Rwg1WESw73bQg7+EJ4VIIJZLLiaqqTEycSa0WPHy4P43GwosfdOqUCGhtaSkE6dln\nyYSEerOaTCWMjZ1IrRbcs8WdSROdaHAC+eij9U6mN5nKeeSI6AkmLxouvBUAEcjawkK89/cX4dT2\n7CHN/2fvy8Nrut7v1703cyKzmIKY5yGoqUWqNRatolpqqKLmUqpa2oaq0tYYqig1tGoeihrr3EQi\nIcgoISJEIpFB5ulOZ/3+2BJCZtH2+/tkPc9+TnLv3vsMd5+zzn73+67XwPfDwghJYuvLl7kiOpox\nJZDb1YwMtrp0ie8uWkQC1A4bVq4sDAaDjgEBr/HqBmPKluZk69aUk5NFMH/LliTAM2+8wVpHj/JK\nMXpjydnJtPjWgmMPjWJy8kmmpl54on+h9W1h8TirgyzLnHBkAuEOHrh+oMg+/f39aWFhQfN65qy5\nrGahQPunERQUxHr16tHc3Jz79u0r+Fxv0HPlxZU0X2pO6++s+bP/z1yiXkK4gzbf2RDuoNMPTvzy\n/JeFiJIkMzWZPHnrJD898yk7be5UoJZiv8KeF6IvFKqblRXOS5daUJKUPBs0l2ZLzTjgtwHFvoB5\nR3uzy5YuhDvYbmM7nr19tuC71NxUzvprFlWLVbRbbsex7mdYrZpMG5vHWun5w+Fu6l2uv7Se/Xb1\no/ESE8IdtFtuR9efXTlo9yB23vAqzdzFeVpM70G0+Y0wSyVMMoimR9nk/bVccmAvk7KSKcsyD4Ud\nossaF8IdfGf/O4xOezatUsG11QsdiTp1xBDu91IeT8KTY5R3uWtXsc2KRRURVqEKlQSDIY9hYWMo\nSeD166Op15cyOwoPF6+zSqVwq5sxo2wK/ffu8eHo5gz4EcKrUzLljRuTmZUVWqiaXp/NwMA+lCQw\nNnaj+DA7W2iPvv66cEG8dq2Q++TehARCkvhlVFSZZ7J5BgPnR0ZyzrRpJMD7EyeWK6RDe0VNXTUl\nc+qoeOD0Ujp+78iFfy+kJjuD52bMoFalYo6DA7l3b0G/siwzJ+cOHzz4jbMPdSbcwW3HxfWQJDAm\nxoOkSIYBkD///Hh/Hpc8CHfwy/NfPnswaWmMioigk5MTXVxc+Ne1v6hwV3D6ieklnsODBw/YrVs3\nAuCECROYlJzEO6l3eOrWKS76exHrrKxTYA6EO9jtl278Pfj3IuXDikJKTgr/ivjrGcJMSNhHLy8r\nentXZ0rK3yTJDZc3EO7gSu+1jIsTeRS9vEQWjXyBHFmWuSdkTwHxdPy2I2stqkUTd0FoLde2Z5up\n3xJtfmPrQRKl4IhnzLT5yLmTw4DBAQydEsqU9BR+4/kN7VfYF3hr5hN3aip56BA5clwK7Wo/fGxK\ntblL2+77ieHvsPmKHsXK4YnjJo8de5zgpHNn8u+TOl6sd5G+LS7xdTdDQWhMeVBeIqxylvkfxJNZ\n1qtQNLTaJISGDkVGhg9cXL5B/foL4Xn0KNycnUUgdVElKkpIe0yZAsybJ9zkSoOPD/D220BODrBx\nI7LebIv7cR5ISPgNspwHO7vXUafOx7C17YGQkCFIT/dGs2ZbUavW+FK7vq/RoI2/P5qYm8Pb1RXG\n5QgklynjbPID3P14Lj76Yw/8Ro9ClzVroXAs2lmkAJGRwCuvQFYRvj8+xBVzA9ZHuyAy4C4a9B2H\nO7XHY0lGBhYu/hrKa4HI6dcKMQsa4qHxVejy4qDTAhP9gBZWdtjs9iGqmXVAXM7vSMw9gWrV1uKV\nV2ahd2/g+HFAoQCkOxL67OqDN5q+gcMjDxdWJdmzB5w4EVE6HeabmOBbf380b94cH5/8GB6XPeD9\ngRoNTe5Cq02ALGtAaiDLWsiyBnpDDiISbmDDhhCcO5gGmgPoD6A1AAVgY2oDBwsHWBhZYMvgLeha\nt2uZr22R11vWISrqM8TGroa1dTeYmx/CV1/VRECAGlpdL8T1HAKDy1lgsz+Q2KagnZUVMGwYMHYs\n4OYGZOsyMcBjAHyyfdAqphVUVCHRORMJ+mTQJPOZ/TpaOKK+TX3Us6mHejb1YHfdDqrfVaieXh0+\n9X1w+OXDyDLKwqCmg/Blzy/RuU7nEn564teDMThwPB23r7rAkFsNANC+PfD666L06PE4aP/SJWD+\nfOEU06QJsGwZ8NZAA26MDUfywWS4ervCrJMN3n9fOEXNmyc8V8syjBWKKmWZKpSCKiIsGdnZYQgJ\nGQStNh7Nm++Ak+o1YO5cqHfsgNuTFY2NAWfnx6VlS+Cjj4Dq1Yvp+Sls2QJMnw7Urw8cPSraP4JW\nm4z4+C24f38DtNr7UCrNIMs6tGjxG2rUeLfUrmUS/YOD4ZOejsBOndCkBMmQrde24peAX5ChySgo\nmZpMEIQCplh7sRWmnw1AnpkpTD+ZC9W8ec+EcQAQLwOvvAI5KxMffdoCd6x9sKgFULPWR9im1iC2\niQJNDMHoZhINc30ynPcBLtsBpQ5QlHAb08oKcdMa4FbfEGzbsQbff/8xatYE/GL90O+3fqhTrQ78\nJvrB2vRR/IRGIzxrN27E9WrVYJqZicYA8OabwKpVyKxTHX23NcG0Bumoa5b3xJ4UgMIEOpnI0eug\nMRDWxgrE3CG++9Ecd27monOvzli/YT06texUrPpOeaHRxCMsbCTS0y+gdu2Z8PZehY8/NoJKBbRs\nqUbTpm4wc0jE79ZtYa2qjhWNL6OmozkMBmD/flEyMoDaDdOgGj4MMRbnMSZoDD7oMwl7ljTELw9q\no6a5Dpt3ZKBBr0T4hvrCO9gbOnMdrOpYITo9GtFJ0bibche5qtxCx9bzRk9MjJ6I4b8Ph3mDsuu3\n6fXC4fncOVEuXgS0WhEh1L07UK0acOwY4OQEfP01MGkSICdqEPpWKDKvZqLRD41Qd25dAMJbddYs\n4KefBOH/8ou49UpCFRFWoQrPgZSU07h+/R0oleZo0/oorE/cBmbPBlJTgY8/Fq+0+cRXvXrZXk+f\nhk4n+vzpJ6EpumcPYGdXZFVZ1iE5+RAePNiJ2rUnw9HxzWfqHDt2DPPnz8fPP/+MXr16AQA8YmMx\nKzISPzdtio9KEJHMl8BqW6Mtmtg3gbWpNWxMbWBtal1QzIzM8auXP6YeDMIIT0/orK1g/Oln4npU\nE2/9SEoCevaEITYGw6fY44T1A2wYuAGv2txAbOyqgv2l6i0RnJoNmjTGqI7ucElrCJN9JwEANDLC\nmmsbIBup8EmPz6AwMRFPvIMHgVOncL+2HeIXp6JGv1W4r+iGvrv6wsnSCerxajhbO4sd3LkDjBgB\nXL2KffXrY8y9e9j9228Ydu8esHQpqNcjY9IrCByoRorKgASzUXin4/fYH3YUWwN/hX/cFRgrjfFW\n87fwoeuH6FXXFbEx3+HevfU4ckSJbdsA0giLFy/G7NmzYfScMnhpaV4ICxsJvT4DTk478dVXw7B/\nP9CrF7BzJ1Cv3uO6pyNPo//v/TGz80ysG7Cu4PPcXGDzgdtYGPwGss2jgGOb4WoYCxMLJS5dAl5p\ncg+N7qzETfkywkzDkJGbAQAwMjJCUGAQbDxtcHv+bUAJ2P9gD81gDWIyYtDMoRlqhdVC6NBQKIwU\naP1na9h0rZj2bXa2CE/NJ8boaEFuc+eKIZThn4HQN0Ohz9Cj5e8t4fhmYcsDCSxdKkJuBw4UMryW\nJUSllJcI//V1vucpqFojrEIpkGWZaWm+jIiYSR+fmrxwwZZ+fs147VpPhoaO4M2b03nnzhLev7+J\nd+4soSQpeflyW+be8BHel4BIJBdUtCdiuZGY+FhNZt68knPmlAG7d++mSqWiQqGgvb09IyIieD0r\ni2aennwjKKjEdcF9ofuoXKxkv139Sl3bMhgMfNvvGNtt2cIjnZqSAPX2diKLe1wc2aED9aYm7D/Z\ngtW/r16wjpSn1/Bz/2/5kvQjpSSxTrnRfyMtvrWg3XI77gnZy9u3xVrXyVsnCXdwR+COQvv2vShz\nlGI308ycKKsUjB4JfvizCRuva1x4je3oUdLWlrKtLZd07EiFQsEdOx73lXPLhw8HiAy12hrmXD+7\nA02WGNN8qTnxNdjru2Y8uOYjZn3rTo4ZQ7ZtKxyPvLyYnX2LoaHDuXcv+PLLpgRAV1fXQp6l5YEs\n6xkd/T0lSUU/v6Y8cSKKdeoI/6rvviveP2n2ydmEO3g49DA9PDy4aNEivjv/XZouNKXxfGN2aPka\n27feRhubSBoZpVKlGkdAhBM0tGrIN/AGv6r7FaXtEm2tbdnNrhvP4zwD+wYyN7roNfDsG9n0behL\nTzNPJuwvWQqtIniw+wE9zTx5sf7FItMqPYlNm8QSfO3aYgn+/PmibyFUOctUoTT8L4RPZGWFMSpq\nEX19G1KSQLXalCEhwxgRMYOhoSN47VpP+vk144ULtgUOGZIEBgcMov7H70RiWUtL4Vr36Kn03Nct\nIICsV0840lTEFe4pbN68mQqFgr169WJgYCAdHR3ZuEkTtj13jo7e3owvQQzyr4i/aLzEmK9se6VY\np4misDTqFiFJ7Lx8Gk83NSIBykol9SolB44C2//cntFp0dQZDNwWF0eXR/GK0/buLdTPzeSbfGmz\ncIrB26MI6xiaTnydJp/X5oeTNfzxRyF9GhwsksnWq0em33nIB+8OIgHm1ATvbHlXdKbVipcKgIYO\nHTi5Tx8C4ObNm0mKl6H79zfR09OSXl7WTD6ykPKjdFRBjawY1q4OtQ52LBQ45+wsdMMaNRIJjB/l\nKkpL8+GVK13p7g46OBjRxMSI588X7wxSFDIzQ+jj8xIHDgS/+qor587No0JBNmtGPs2rT4+5XF0u\n225sS4uvLQhLEO1ALAIVMxS0dbJl/br12axZM7Zt25a9evXi/Pnz+eeffzI5WXhyJh5MpE9tH0oK\nibOMZxEAt03fVqojlSZRw6vdrlKCxOgV0WUPISoBskFm1KIoSpB47ZVr1CSWLYfU2bOPw2MB0sFB\nOGkfPy70TzUaTRURVqF0/P9KhBpNIqOjf6C/f/tHxKZkYGAfxsdvLzHswWDIY27uPeb4HqT80kvi\nthg4UMQBPoHnum7Hjok719mZ9PcvvX4pWLlyJQFwwIABzM4WRObt7U2ViQnRrh33PQoILwqedz1p\nttSMrj+7Mi03rdh6xWFDbCwhSax+age7f2jCI62N+dZI4SKfnpfJ3x48YBM/P0KS2NHfnyeSk5+5\ndlotOWKklnD7msqvjalyNybcwTpjFhZEhBTEuSlElnefez6stqwaR31chzkNrEiAWYPbkq+8Ikhw\nyhSOHjaMAOjh4UFZ1jMn5w6DggZQksCAgNce67zq9eSmTZQbNRIz/g8/JNeuFTt6+PDxgd67J1i4\nenXyxg2SglgTEw/w1CkX1q8PWlqqeP78mlLJwWDIY1TUVzx3zoivvGJCoDkVigACIty0qBSJRY25\noxePEgtBq4VWhDvoOs6V6j5q6jLKZl3Qpet4a/YtBr4dyJZNW7JBgwbMLUO8qD5Xz9CRoZQg8cak\nGzRoyqjQXdQxZOoYMjSEEiSGTwivUF9ZWSKx8NChcTQ3P0hgHpXK7lQqTauIsAr/m9BqUwtmf1eu\ndGZMzBrm5cWXrXFeHrloEWUjIxqqVxeyJZWZASI3l6xVS6gTx5fxmIqBLMt0d3cnAA4fPpyaJwLS\nvdPSqPjiCwLgBx98UOSD+cr9K6y2rBqbr2/OxKyKKzZvj4+nUpLY6uJ5dtnWm0s9l3FvQgJbXhJZ\nH9pcvszDiYlFHoNGQ779tnj6/PCDiF9rvLYx4Q6afWPG+WfmMyI2iX5+5M6dYmboc8+HVsus2GRd\nE8amx9KQk8WE6a1pMAb15ireXtqCAwbYEwBnzKhGT08LShK4eXN7enj0ZkjIJsqyeNjmROUwxiOG\nQf2DqDZVU22i5gWHC7xY/yLVLa7Qo/ktjndJYGu7bFoYGziy3Q1mWjgxp3pdZoQ+joUzGDT091/B\nGjVUtLMDDx9uycTEgwX7eRJpaRd56VILnjsHDhxYn0BzmpnlUKFIYosWn9FQxrQPsiyzV69eNO9l\nTriDA4cM5JVBV6jPKXus55M4d+4cAXDpkxI9Je3fIPP2F7cpQaKXjRevj77OxAOJ1GWWjYTzYvOY\nsDeBl9tdpqSUeG/1vXLPLmNiYujh4cFRo0bRxcWlwPRrZGRCJ6fuNDefW0WEVfjfgyzLDAl5i2q1\nEVNT1eVrfOkS5UdBTNv79qXT0aPsHxTELffvF6t6Ut5jC922jauHDePKv/9mdDmVWp7u65NPPiEA\njh8/vpA6SoZOx4a+vmzg68vPFi0iAC5fvrxQ++uJ1+mwwoH1V9d/Jn6tItifkEBjtZrtLl9mu8uX\nCUli80uXuDchgYZiHm55eeTgweLJs2aN+Cw2PZZGS4w47vA4vn/ofSrcFbRaZsUvz3/J1NzUZ0gw\nHwaDjlHnx/PakWYcOrQGAXDmzDa8cWMSw8PncerUC4VmljWsdOxsmcbhuMd5COcvdUPo9+Ft7hx5\nn1M6JrN99WwaKWQCpJHCwHbmGRyiiGVb2yx2VF1jKmx4A035WpsEfvyxmI0kJ5OhoUG0s7Oks7Mx\nDx4EL19uzYSEPZRlPXW6TEZEzKQkKejt7czRo/sScKKdXSpr1CC//34/AXDDhg1luuY7d+4kAK4Y\ns4K7bXcz5J2Q55qZkeTbb79NCwsLxsSUfUw8PPuQ4R+E84LDBUqQ6GnmyeDBwYzbFkdNkrhvZIPM\nzJBMxm6M5fXR1+nr4ksJEiVIvGB/gcknk0vZy7OIj49nrVq1CIC1atXi8OHDuXLlSvr6+jLv0VKA\nXs8qIqxC6fj/zTR6796qRxqgq8reKCeH/PRTykolk5ycOOC77zj95k3Oj4xkw0frWipJ4msBAfwp\nNpbxeXllvm6JGg13P3jA8eHhrO3jI/LiPVG6X71Kj5gYPigD0Wbp9byQmsq1d++y+6hRwhz64Yc8\nkZjIC6mpDMjI4Jn712l/ZAVx/m+OObeCe0L2cODQgQTAAweE0kpUShRrr6zNmj/W5K2Htwr6j4mJ\n4fLly/ntt98yqyjbXCk4kZxMM09PNvbz4674+ALd0HxotUIB5vRpibm5j/2Pnnzuf3b2MyoXKwsk\nuq4nXueIfSMId9B2uS2tllmxqUdT3s+4/8z+ZVnmtGnTCICLFi0iScbfl9nzJR0BckTDh1xhGcrJ\niGQ/RTxbVMummbHhGS1NlUpItn3+eeFA9diNsZQgMfjj2/Rf402tkTkjrFxZwyytQBPz5EnSz8+P\nFhYWbNPGhX//3ZSSBF661JwXL9ajJCl48+Z0zpgxhYA5a9eOoYWFsJDLssw+ffrQysqK94oQX3hy\nzKWkpNDJyYmdWnXieWPh4CLrn99ycefOHZqZmfG9994rd1uDzsAUKYURH0fwYr2LguiUEv07+vOC\n7YUC4vOp6cOQYSG8t/oe0/3TadCWn7x1Op2YDZub08/Pr8SZZHmJsCp84n8Q/z/FEaan+yIwsCcc\nHAahVatDZYvt8vYGJkwAbt3C/jffxJRJk7Dc1RWTHoUZkERQVhYOJCVhf1ISInJzoQDQ/OZNNO7e\nHRZKJSxUqme2KTodzqam4lpWFgDA3sgIr2dkoO+GDYhwcMDZiAhYtG6NmMaNca9xYygdHdHbzg7v\nOTnhbUdHmCmVCM7Ohn9mJq5kZsI/LQ1hERFgZCRw/rwIvn//fXHsRZxn9eTTSAn7AQYaAB2g2KmA\n4oECg78bjBDjEKTmpsJzvCcaVWuEI0eOYPv27Th37lz+SyUaNGiAzZs34/XXXy/Xb5Ci08FapYIS\nSkREiJRIV66IbUAAkKdMgtL0FMytX0J2jow3hxowfryMuvVk6KlFv9/6oW+jvtg7fC8SExMRHR2N\n6Oho+Ib64ojfEaSnpqNbnW4wVZrCYDAUKmlpabh8+TJmjpyJOa3mwPO4HvP86yGTRpiDCLxZNw12\nr9vB4Q0H2PWxg5G1EQwGEWVx/bqI/2/RQkTF5EeCPI2I6RGI+ykOzbc3R80agcCQIZA7d8Glxacx\nbZ4FQkJEbFvNmqcwePBg9OjRA9u3f4jExFUAiCZN1uP7709g2bLlaNQoEFFRrXHkiAJDhoj+79y5\ng9atW+PVV1/FsWPHCo3hJ+/VadOmYdOmTdjqsBXNrZqj45WOMLYvJaCujPj666+xZMkSeHl5oUeP\nHhXqgySyArKQfCQZaZ5psGhmAZuXbWDzig3MGpo9d9zlggULsGLFCuzYsQNjx44tsW5VHGEV/meg\n1Sbj6lVXKBQm6NjxKoyNiwjyfhJZWSKHzPr1yKtbF+/PmYO/O3XCwVat0LuYOD6SuJ6djYPJyTif\nmopMgwE5BgNyZLlgmyvLAAAjhQLdra3R194efe3s0MHSEqq2bRGj16Px3btwcnJCcnIy8vJEELdN\nnTowtGyJrBYtYNSqFajXwxAZCURGwuj2bTAqCoZHdU1MTPC5uzvGz56NLIOhoAQl38K8vxfhrcZv\nYv9r02CQdQhLCkNwQjAu3riInTN3QqPRwHaGLZa/tByXT1zGvn37kJmZifr162PcuHEYO3Ys7t+/\nj0mTJiEiIgLjx4/HypUrYW9vX+pvEBMjSMDLSwRQZz4SL7GwADp2BBy7nMZRy0GQFfoS+6lzsjke\nBt0tuDb5sLa2Ro0aNWBkZASlUgmVSlWo6GJ1aB/fHqPl93EQdbEJDeFso8evCzLRbZQlzOqZlXoO\npUHWyQjuH4x073S0l9rDJvY08O67QP/+yNh5BMNHmeDsWWDJEsDF5TeMHTsGw4YNw969e6FSqbBs\n2TIsXLgQbdqcQ0jIa1i3Dpg5s/A+Vq9ejU8++QS7d+/Ge08nAwTg7++PLl264N1a72JK6hR08O0A\nq3ZWz31u+cjJyUHz5s3h4OCAK1euQFVE2qx/E0ePHsVbb72FyZMnY9OmTaXWr4ojrMJ/F3l5IhV2\nSMhzdyXLBgYFDaBabcKMjKulN4iKIpuK+LcbEybQ7q+/2NjPjzeyyx46UBwMssxsvZ65Twd/HTpE\nApzy2ms0NjZmdHQ0NRoNL126xNWrV3PEiBGsXbt2wWJ/frG2taWbmxtnz57N7du3MyAgoGD942kM\n+G0ALb+xI8zS2KgROXWqyHyUn/EoJCSE1apVo4mJCQHQ0tKS48ePpyRJNBgM1OuF6fLWLTInJ5df\nfPEFVSoVnZycuHfv3iLNT7Is9LzfeUeYFJVK4Xg5dSq5bZv4efXVsX39AAAgAElEQVR68m58LE0X\nWBAzQLQB0RpEKwXR0pmq1n1o0mYWjVp5EM7eNDVNZf/+u7l27ToePXqUgYGBTC0lDVRWWBYlhUTf\ngaEc8nIeAfKttwon66gsaB9q6dvIl95O3iLebvNmYVPt0YP6Dz6kuvEEbsUH9GkyjiEdO3EHQL8m\nTXixf39WB9ip004C5OzZRfev1+vZuXNnOjo6Mikp6ZnvOnbsSCdLJx7HcT7Y/aDyT5Dk3r17CYA/\nPynk+h/ArVu3aGNjw44dO5bJu5Usv2n0Xyez5ylVRFgx/GtrhMuXiyGnVAp39RJc/EtDfkaIAvHp\nkhAcTNaqRdnOjlt37y7Ib5f8RH67sqBc102WyU6deLdePRobG3Pq1KnFVJMZHR3NvXv38siRI4yO\nLnuMlne0N+EOmr62nG3bkoMGidBHQARm9+gh8vWtX3+Ogwe/ye++28FduzK5ZAn57rsiXtzUlAXr\nZI0aibSJP/0UyA4dOhIAhwwZUpCbT6Mhf/9dkB5A2tiI8L0no0y0WvLUKfLtt4OoGGxDfAWq6k/m\n5MlbGBUVxYcPH1L71HW/do3s0kX02bNn2d+Tro8O40aza2zaWKZKJd6xKtPZ92lkhWXRy9qL/u39\nqc/SCwVwZ2eydm3KdeowtZozo1GXD8zrM9nahlEADQDzFEbciI845fVbJSbyCA4OppGREd9///2C\nzyRJ4vr16wmAX+JL3ppzS5zkX3+R48eLbSWddL5HqoODAx8+GULyLyInJ4ft2rWjnZ0d7xSTwaUo\nVDoRAjgE4A0AyvJ0/E+UKiKsGP4VIkxMFIHJ/fqRn3wi8tSZm4uMCellSG30BFJSJEqSktevv1ck\naeQZDIzKyaFXairPHDvGXGtrptaowbH79xOSxAnh4dSU0V39SZTrup0+TQKc1KMHTUxMSvTIywrN\n4tWuVxk+PrzMbvCyLLPH1l40WlCDNo5ZBVmeNBoRCvf552SHDo9J7unSoAH5xhuCyLZtI3/6Sfxv\nZia+t7DQsVWrH2hiYk4rq/rs18+TNWsKJ5OmTYWzS2ameAbn5oowyfHjSVtbmcBWoqGIC+zuPpJZ\nWaVfO4NBTLLs7QWJz5sn+i+qnp8fOXuilrWRI7xBa5BqdZku23Mj+UQyJYXEkGEhlA3Pjr2NG/Nn\nyDKnTPmKk3pM4zbVh9QoTCgrFOSwYeIEisGXX35JADx58iRJ8uDBg7SxsmFHZUde63WNhqsBZJ8+\n4kfKzzn56quVEptKihRUSqWSM2bMKL3yC4Ysyxw/fjwB8MSJE+Vq+yKIsA+A3QCiACwH0Kw8O3iR\npYoI/w9hxgxhRwsLE/9HRZGjRokh6OhIeniIp3gpyMuLp49PTfr5NaNO9zifnUGWOTMigtW9vQu8\nMwd89x2zTU15o25dNt+7l838/Lj6XvnjlsqCvLzH+fFIkr16MapGDRoZGXH69KJT/siyzNj1sfQ0\n8yzwsLvS+Qrz4kpP5XMm8oxQZenswcOHi6+XmChmcV99JcRsrl4tOnA7Hzk55IkT5LRpIo4cuE0g\n5hGBnqFSuYoq1VUaGYlA9yfJ1do6i40ajSNMQLMFZmy4siFvLL1B/47+ZXaVT0oSxoJ8cZcDB4SZ\nVa0mZ84Un4nwBpmdlQ/50486/tOTl3s/3qMEiVFfP5svkhRKb+bmYoZdo4ZQaUsMihNvJ7a2LJj6\nHjsmmP0J5OXlsUWLFqxXrx4zMjL43vD3aAxjHnHcSP2oDwTL2tmRq1eLN4W1ax/npHz3XfL27ec+\nv2nTplGlUjE4OPi5+yoSGk2BUk9J2LJli5gJf1lEeq1S8MJMowBsAUwBEAvgIoAPABiXZ2eVXaqI\n8P8IbtwQr/lFmQf9/Uk3NzEUGzcm9+wRrFIEZFnPgIBX6elpzszMwjfpZ5GRhCRxWEgIF9+5Q2n9\nehqMjJjTvj3T799/IeSXD52O7NtXEMPnn5M6tTcJcEKXLjQ1NS0wLT4JTaKGwYOCKUFiUP8g5sXn\nMfFwIj0tPelTx4cZV4tOWksKAm284iVidj1Om1W2/HcVgSyLn0xMOm6zbdvJNDa2IADWqdONb731\nGxcuzOOSJeSmTWFs2bIVFQoFXee7UvG1ghsabaAEid6O3lQbq5l4qOwB/D4+wnQLkNWqia2ZmVgD\n/OVHDY8pLwgz4b8AWZYZPj6cEiQm7Ctae9PXV/CTre3jdz+SZEYGuWoVWbeuOCk7O2El+fprYeZM\nTqaPjw8VCgVfdXuVFgAPKNpRNrcUM8A5c/gM86enC8uKubmoM2uWeAOqIJKTk2lvb89GjRoxpBLW\n8wshPV3MYAFy8uRi7/WrV6/S1NSUffr0ob4ciaHz8UKIEIADgNkArgD4E8C7ANYDUJdnZ5Vdqoiw\nYvjHTaNvvSWeZgnFCPbKspiG5GfnrFaNfO89ct8+6lLvMzn5BCMjP6W/vyslCYyL+7VQ8/WPJL+m\n3LwpCG/tWtGPm1u5za7FIS03jfM3z2eu7tnF+unT88lCbL1tB/KmjR1VKhVnzZr1TP2Hpx7Su4Y3\n1SZqxqyJKWRiywzM5MW6F+lpXrzA8WavI4Q7WP+trcU9RyoFoRc0NDWWOahpBm9Ou8mYdTGMOhTF\n77/6nk2aNCEAOjk5ccqUKbS0tKSjjSM/7vuxyEg+8B3emHSDWaFZ1KZquanlJkoqiQ9+K7ujh04n\nluHGjyf37XtsKr0x8QbVpuoyzZxfFAx5Bl7tdpVqIzWjvo4qMqg9Pv4Zlb7H0GrFS9+kSWSbNmKm\nlz+1btyYl5s25VcAD+DRtHv4cDIysuSDun9f9KdUintoxYoKrx/6+PiwZs2atLCw4J49eyrUxzNI\nTCQ7dhSWoREjxHl17kw+tWyQkpJCFxcXOjs7M7GChP4iTKOHAYQD+AJArae+u1qenVV2qSLCiuEf\nJUK1Wgyzb78tva5eT93Rvcwd3Yd6O6GoazAGk7qD4QtUDDzfuSBTeT4OJSZSIUkcEhxMvcFAfvml\n2N/QoWLxqhKg0WvYe0dvYhz42o7XmKV5bFv08BC7mzdP/H9qeQAJ0FXpSmNjM8bFxRXUNeQZeGvO\nLUqQeKnVpWKV9jUPNLzaXQgc31l8p9BsNk9joMXcNlTOasobEc+XueJJyLLM7FvZjNsWx/Dx4bzY\n0Jed8JCW0PGQuS+9bLwKgqMlSJTMJa5rtI5uddyogILtzNtxp8lO1vqkFhu4N2BqXGGPz3N/nWPA\nqwGUFBLvb342ML6syL2bS7WRmhEzIp73lJ8b2hQtr4++TgkSL7e5zHT/53jpysgQi7vffUe+9RZ1\nNiJLxhGr2qS3d/n6Cgt7LN9TAbNiPuLi4vjyyy8TAOfOnVtIyajciI4WquJmZkIdmxTSPFZWQsdV\nkpicnMxvvvmGNWrUoLGxMX19fSu8uxdBhAOL+My0PDt5UaWKCP/jMBjITp3Ewk5OTqGv9PocZmRc\nY3z8Lt6+vYDBwYPp69uAkqQQ2SLOmTBiSzumje9MQ23xUKBKJfQ6O3UiO3ViZocO9G/enKGtWlHf\nubN4swbEItNzpjfKhyzLHHd4HOEOfnDkAyoXK/ny1peZlpvGkyfFy/eQIU+kzRkxgjcsLAkoaYqZ\nnDs8iw/OpDLxQKLQV4TEiBkRpTrFGPIMDBsbRgkSQ98JpT5b1B+0YDfhDs7a/EelnF9OZA5vTr9J\nn5o+j+WvHC7wx053CZDfz82hQWegLMvMi89jqjqV93++z1uzbzGofxB9XXz5F/7i5Q6XOWH1BCrc\nFQUpmJ6GPkfPoIFBlCA0JiuCm1NuUm2iZm5M5bzkVAaS/kwSGR2UEiM/i6yw7mc+skKz6GmhZmCn\nv2nIq2Bfsvx4sfVRFo6KQKPRcMaMGQRANzc3JhRn1SkJYWHiGWBjQ3p5Ff4uPJyahg2pVyj4qbEx\nAbBfv368cKHoMVRWvAgiDCjis2tl6hzoD+AGgFsAPivi+9EAggAEA/AB0LasbVlFhP99/P67GGI7\nd1KWZaak/M3Q0BH082tMSVIWpD5Sq4156VIrhoaO5N27S5maqqZe/8SDTpbFWuLnn4usEAMHMqtv\nX57p2pXqrl2p6dtXrLP06ydCNCpxPXCxejHhDrpL7iTJ/df303iJMVuu6UArpyS2aydMdgl7Eni1\nvTf9sIv9lK/TFKY8iIOFZlHe1b2ZfLzs+oqyLDP6+2hKCiFZ9eemdGJmYzosbEtDEcLO5UH6pXSG\nDg/lbvvddHvHje3mt+OG1RuYHprO9DSZtWuTrq5le58w6AxU31ET7uDsk8UEyuXX1RgYMkxkHbi7\n9G65jjk3JpdqEzVvTrlZrnb/BLSpWoZ/KNYN/Zr5Mc27YsGMujQd/Zr60dvJm3mxz2n61WqFpp1K\n9XgWVkHs2LGDZmZmdHZ25qVLl8re8PJlkSepRg0yMLDgY1mW6enpySFDhtAa4OFHnlepAwaU7M1V\nRlQaEQKoBaDjIzLq8OjvDgDcANwotWNABSASgAsAYwCBAFo8VacbABs+Jj6/srZlFRFWGP+IaTQ3\nl6xXj7KrK5MSDvHKlS6UJNDb24khIcMYFfU1ExL2MSvrOg2G8sXzPdBo2MDXl9W9vRn51EyzRERG\nkuUIoN8RuINwB8ceHkv59GlKNjZkjx48OGcYVYtMaDqrKS+H3+fdZXeFudP2EI8rp1OpUHJit4mM\n8Yjhuc8fsI/dQ7YyzuBPP+oqxNFJfyZRbeXFM4rznNl5Jg+o/yx/JxQiyEnHknit5zWeMjrFD/p9\nQNOvTWmx1IJNPZoS7mAzj2bsN38nodSV5OVfCFmaLDZc25CN1jYqNrfhk2POoDMw7H0x2739+e0y\nOzJFzIyg2kjN3Lv/ndng03h45iEv1r9ISSExYlaEiDcsI2SDzJC3QiipJKZ6CtPyc9+rmZkijsbC\nQpDSc+DatWt0cXGhiYkJt2zZUnqDc+coW1lRW7cur+zdyz/++IM//PADZ82axU6dOhEAHRwcuGjR\nIsbHxQmzsFJJtm79lAt2+VGZRDgegAQg89E2v/wJ4O1SOxYkd+qJ/xcAWFBCfTsAseVpW0WEFcM/\nQYSG5d+RAMM21Kckgb6+DRgbs5EJR2KoTS4f8T2JTJ2OHf39aeHpyctldYSRZeFurlIJj5YyxBBK\ndyQaLzHmq9tfpeZhIunsTKlGDRo6d6FWYczzLqDlF2C9j+34h80fvN7+AA0qc45u1owWFhaFTEgJ\nCY/Fpvv0ESnuyoP798k+L2VwTtsveU55jl7VvHh36d0yP2R16TrGbY3jpRaXeB7nufzl5ay7uC7h\nDo7cP5Ix6TE0yAbuv76fTVe1JdxB60WNuPXaVmr1xf9Webo8Bj8I5vgj4wl30POuZ7F1nx5zskHm\njY9uFJiKS8ugkBeXR7Wpmjcm3ijTOf+b0GXqGDEjghIk+jbyZfrlso3T/BeqJ83GlXKvxseLGI7q\n1Ut3uCkFycnJ7Nu3LwHQyMiIlpaWtLe3Z61ateji4lKQFHhugwbMAxgEsCYKKydZWVnR1dWVP/30\nU0EuzQKcPi2CSe3tn81SXA6UlwhL1RpVKBTDSB4ssVLR7YYD6Edy0qP/3wfQheTMYurPA9CU5OSy\ntq3SGv3vwWDIQ+J1D1Tv/hnS2hJRa1qhfv0v4Gg/HBETbiPhtwSorFSoM7MOnD9xhomjCUghcn3s\n4UNczcyEnbExahgbo4aJCZxMTAr+djQ2xoc3b+J0SgqOtm6NQY6OpR9QTg4weTLw++9Au3ZAUBDw\nww/AvHnFNglPCkf3bd1Ru1pt+Ezwge2s+cDWreBFX4zb0Bn7duXhxMKriFf7YOor36CaDpB2ZEHO\nMEYrvR6ffvopVqxYUdBfRAQwfbrQ49RqhV62k5Mo5uaimJkJ0Wdra8DGRhQzM8DXFzh5EtA1Ogz2\nmYfTAzaj9qYaSD6SDJNaJnBZ7IKaH9SE0kj5+DfINSDjYgZSz6ci7XwaMvwzAAOQ/HIyfnrzJ0g5\nElpVbwWPAR54tcGrBe1kGXilh4xQ3TE0/OAbBCVeRX2b+ljwygJ0qNUB4UnhCE9+VJLCcTv1NmQK\nndU5XedgVb9V5RorJHF73m3EroqFeWNzNPyhIRzfdCxSnDnyk0jErotFl4guMG9oXq79/FtI80pD\n+Pvh0MZr0WBZA9SdWxcKZdHylylnUhDcPxhOI53QYneL5xaofgY3bwLduwMODsDFi0BZ7p1iYDAY\nsG3bNty5cwcajeaZ8lp4OD4MCUGUkxMOjBuH6k2bwtnZGXXr1oWzszOsra1LPr+oKOC114CUFDH4\nu3cv9zFWmui2QqEYQ3KXQqGYC8HkBV9BsG2Jo16hUAwD0L8sRKhQKF4FsAHAyyRTy9q2igj/O5Bl\nLeLjtyI6+hvU+zEedf4E0rzWw7bbVNAA3BhzA4l7ElH307rIu5eHpH1JoIUSN96zgMdQLcIttFAA\naGpujiyDAYk6HXTF/LabmjbF5EeZIkrE3bvA0KGC/L75Bvj8c2D4cOD4ceDyZaB9+2eaJGQloOvW\nrsjV5cJvoh9cLkcA/foB8+fjO9sV+OILYPl8DV47F4KsoCxo12oxOmc0VFTA1b85Lpy8hrt378LR\n0RFaLfD998DSpYLsxowR9/a5c0BCAlCrFtC8OWCgHlG1VsCQ6QRF4ARkpqsKxKufhqkp0KwZ0Li6\nFtVvJqNmbCqaNZDR/Yvq4IM8pJ1PQ/rFdFBDQAVYd7aGcW9jbGu0DRtiN8Dc2ByL3RZj+kvTYawq\nnLlg61Zg4kTg11+BceOIU5GnsMRrCfxi/QrqGCuN0cShCVo4tkDL6i0Ltm1rtK3ww/vhqYe4Pfc2\ncsJyYOtmi0arGqGa6+NUENoELfwa+MFppBOa/9q8Qvv4t6BL1eHmpJtIPpgMuz52aL6zOUxrmhaq\nk3s3F1c7XoVpbVN08OsAleULErz28REE4+oK/P23UEavTBgMwCefAOvWAW++CezeXfF9xMSIY42L\nE/drObPlVCYRfkRyk0KhcEfRRLi4lAPpCsCdZP9H/38OQCa54ql6bSFk3PqTjCxnW44bNw4uLi4A\nAFtbW7Rv374gbYlarQaAqv+f+j//s8rojzSgRYs43L37Nfz87sA2swnGLYkCJk6C58iRkPUyamyq\ngaQDSXgwOQGB/YwR3qQJbgak4KU1AXANANqYt0f2ODvoXo1DdSdzuLm5gSSO//EHUsPD4WIwICEq\nCt6xsXBKS8NCa2tg6lSoa9QATEyKPr5z56B++21AluG2bx8Mvfthu9t2GNI06HXvASysUxAw61WY\nNamGPsP7QKFQ4NS5U5h9ajZi7GPgOd4TWQEJ0I+bgA4qe4xqEYDTnj/jra7NMD/OFrqHOqQuSoVN\nVxvUaFUDbtvckBiUiJ7KnvD8zRMXLwKjRqkRHQ2MHOmGNWuAGzfE8fXoIf7//HM1zGwy0eAzDwRn\nnwXuALXNG8Py1nbc+vtlNGmiRts3LuCE4RjM9bXxpmI0cpKrIzvbDWFhwJ07EsTt6AYTGDAEu/F6\n4xy89uZrsOttB3/ZHydjTmJP9h4kZiein6ofJnecjLcHvP3M9UpOBho2VMPFBQgKcoNCkf/7EkYN\njZCck4zMiEzUtqqN1197vdzj5emx9/T3sl7GwXkH8eDXB2iT2QY1x9fEvTfuwcTBBHX/qouYlTHI\n25EHM2ezf/3+Ke//vXr1QvyWeOyfuR9KcyVG/TEKDgMcoFarYdAYYPOFDXJv5yJ7ffYz5xcYGIjZ\ns2dX3vF4ecHN3R0YMgTqmTMBlapyzjcrC+q+fQFfX7h98gnw/fdQX7jwfMd78CAwdy7cEhKAI0eg\nNjUttr5arcb27dsBrRYucXFY7OlZLiIssw21vAWAEYDbEA4vJijaWaYehFNM1/K2ZdUaYYVRGesO\nsiwzMfEQL11qSa+/wNDfmzHj14WUe/UqCJ43aAwMGSo8BO+tvMcZERGEJLHexYucfvMmTyYnMyU0\nQzhOKCV6mql5q89h5o34iKxfnwUBxnZ2Ikbhxx9FeZRFgg4OIoDvyYV1WRbqy0qlCNCPEPFmETPF\nms3V7lfpbXO+kDenl40Xj/c+TrfP3Kj4WsFln27j6iEJPGj1JdPRkK/hIlu3MHDq63/Sy8aLPjUL\nK7+cPXuW9g3tqZqqItzBdp/OJVRa1qtXsrPecd+bNJ3XlPjSmJ2n/MKOY/cSc5yFRufKURxzaCzh\nDvb8tSfjMuKeaZ+dTQYEkLt2GNj7JW2BWEdunoF7Qvaw0dpGhDvY69de9Isp2fNl4kSxhFrZQiL5\nKOuY06ZqeWvuLaqN1fS09GTUl1H0tPTk9dHXX8yB/YPIup7Fy21ECM2tT27RkGdg+AfC0zTpWFKR\nbV7Iev66deL++eijMq2Xl4r794WLsVIpRGsrE4mJZPv2Qpv46NHi62VkCIX5RxJ2qERnGY8Syroy\ndQ4MAHDzEdl9/uizjwB89OjvXwA8BBDwqFwuqW0R/VfOxa5CmSGfPMnsBe8zabAjU9uCGgfVY8LK\nLx4eNOQZGDxYSIjFeMTw66goQpL44ZVbvH9fFt6TSUnk3r3k5MnMdu7GMCyghHP0xClGNllJzbcb\nhMv10zerLJPnzgkBY5XqsRfKgQPkyJEsUOJ4JEWSdCRJPHxmPyZMzaRPede0DX+cM5edP+8sdDvd\nwVmdZxUOHM8vClEutbhU4LWo1+vp7u5OhULBli1bcuXaSFqMmE64gzUXdeX1+3eLvY5nIs/Qdrkt\nHVc48gN3LxoZifcH92+z+NHR6VS4KwpIrDhPzCeh15MLFpBocI6WczoS7mCbn9rwr4i/SvXKPH+e\nhUQB/gvIvpXNkLdDCq59Vtjzu9T/F6DP0fPm9JuUIBVkdI/6smjN0heKzz4TP/ro0SLMoqIIDBQx\nglZWQiLuRSAlRSjQGBkJiaEnkZkpQqYcHMT5DBlCXrtW6V6j4x5tny7jyrOTF1WqiPAfxOnTlOvX\nKyA7jb2Cms5NKI8fJ1Rj9u4VQrrp6dTn6hk0QAROx26M5bqYGEKS2OVgGF/DGf6AuQxUti/oK9fU\nmvdch/DOnLVM2BPIsPevixmihScjP4ukJqkEMe7798klS0hnZ6aYgd71wJvL5jI1J4WyLDM3JpcX\n7C/Q39WfhjwDdQYdT906xVH7RtJ8kSAb008aED2XsFrdKI4ZZeChNQ+ZUeNlpjgPZsLOGMZ4xDDq\nqyhGfRlFbYp4aCQkJLBPnz4EwPffH8Np08SMrF07ctnRfay2rBrtltvx2M1jhQ5XlmV6XPKgarGK\nrX9qzTupd0iKSW1iInny1knar7Cn1TIrdtzUsSCk4dStU8zUZDIjL4PpeelMzU1lSk4KH+Y8ZFJ2\nEi/FXmLfXX0Jd1Axpx7teu2k76WSvUr9/IT6HSAm4EVle/i3keqVysSDFdfN/K8i6UgSL9hfYPCg\nYMr6F5g7qjjIsrhvAbJ//4rF7p04IQjQ2blQjOALQXo6+corYta5c6cwh/z4o/CEBUR88RPhIZVG\nhP8XShURVgzlMrd4eZFNmlAGqDcFIyeD0bNr02AMoTT9lDu2PkfPwD6BQkpry33+9uABIUns8ccZ\n+itdSYB6IxPedH6V25ss5bA6vjRW6Aomk0ZG5AcfkGGnsnh91HVKColeVl68/cVtah8W/+aamBbH\nusuqF8zs4A4aLzFm9c+rs/HUxnx57cts5d6KNktsxXeL7OgwaATVzkb0dHyTu3bKj8Vvpk4VCto+\nPkVetwsXLrB27do0NTXlpk2bOW+eTEBoHee/XN96eIuuP7sS7uC80/Oo1Wup1Wv50bGPCHdwyB9D\nmJH32LyqN+j51fmvqHBXsO3GtoxIFibd4zePF5g4Syv2K+y56uIqXrqay/r1Ra7BHTsKXydZJs+c\neayLamcnMlMklz3Ov0L413Jg/oehz9WXSoIv/Lpt2SLIpUuXsg8CvZ5cs0a069BBvIz+E8jKInv3\nFvdmfsaNvn2FwvlTqMwZ4dpH22NFlD/Ls5MXVaqIsGIo083l60u2bEkClAE+7OPIC0fA6OgV4kbw\n8BC2PDMzYZrQapkXn8drva5RUkiM3x7P40lJVJ0/zx4btzDX2Jj3zJtQs3XXM0HtGo1IUPHnnyLV\njpmZuMfef58MOZbF0JGhghCrefHO4jvPxJzpDDr23tGbZkvNuCtoF3cG7uTKiys5xX0Kew7pyRpT\nahOTFMQsEO+CaOHAanY/cN68TCZ9vlLcBvkBwvl2wjlznrkk58+f5/fff0+VSsVGjRoxICCAX30l\nqk+b9qygTa4ul1OPTyXcwW6/dKPbdjfCHVxwdkGBMkymJpM7Anew2y/dCHdw/JHxz5hCc3W5/OXq\nL1zhvYI/+PzAH31+5KqLq7jadzXX+K7hOr913HJ1C9NyH6uZJCU9Jrs5c8Q13r9faB4DZO3a5MqV\n/9wssIoIK4Z/5LodOiTemlq0KDnIVacTs7H8NfohQypFBaZcyMkh33lHEGAJMmyVSYQdH23diii9\nyrOTF1WqiPAF4Pp1Yd/Ln6K1aMF7Jz+kJIGRkfML142NFeLWABPrj+EFG4meZp588Fs8vc6epdmZ\nM+z4888MsmzBhc6/MjWpbPqf8fHk3LlCDEOhEOP+2sHMAmku//b+zAx5/ASff2Y+4Q7+cuVXBgeT\nv/5KTnI7zx7oSUBBwIzAdJqZRbF795Ns3boXAdDe3p7uX3/N5J49xc4CAkTG2saNC5F1XFwcT5w4\nwcGDBxMAhw0bxrS0NC5bJi7RhAkl+xzsCdnDasuq0fQbU+4K2kW9Qc+zt89yzKExtPjWgnAHG65t\nyG3XtlVquiitVsxSAZETGSCbNCF/+aXY7DdV+F+FWi0GibPzU3mjKAhw+3ZxXwAiP9aBA5XjaPOC\nUOmmUQCzy/LZv1GqiLCSERQk3gwBQQjnzjEmZi0lCQwP/7DIh7QuTcewV0+LpLLYyKwRcxnwzju0\nPnaMTX/7nVNq/8LG9TQVsp4kJgp5USsrcUhDh5JHP0vi2X0He6sAACAASURBVGre/Ful5sou99hx\n9H7CHTQfPoWATOAcVehNALSAFbt0WMD16xN4/foTwtgkL168yCFDhoh65uacbWrKaBMT3gZ4YMkS\nfvHFFxwwYABr1qxZoIhhYmLCNWvWUJZlrl4tjmnUqML9Fod7afd44uYJLji7gM6rhGeozXc2nPzn\nZHpHe7/QfInbt5Ovvy78DCqQ2q0K/ysICBCaoPb2YgFZqyW3biUbNhSD3dWVPHz4P02A+XgRRFiU\n6HZgeXbyokoVEVYMRZpbdu0SST0BkSSUZHz8LkoSGBIylAbDs7O5FClFeL6pJEZ9doOG6R8zwtmZ\nTkeOsM6pM2zYIZ2OjuTN59RIfvhQrGPZ2IjDs4GG3yCEOxx30PQLCzp88hKHjQxm/fo9CYAOJo6c\nopzCWPWzCXGfRmhoKMeOHUuVUllIBkqlUrFt27YcN24c16xZQy8vLx5/FAuxcaM4jmHDyihKLRs4\n9rAIhVAtVvGN39/g3tC9ReY2/P8VVabRiuEfv26RkWSjRsJC4uIiBnrHjiJ04QW+rFU2KtM0+t6j\n9cC0p9YH1QD+Ls9OXlSpIsKKodDNlZ0tbHv5ptDhw0mSycnHKUkqBgT0LpwJgmKR/9bcW5QUEv0a\n+zHNV6xNJWu1bODtTQevC2zWJ4uWlmR5hOpLQ1qa6O/ePTI5I52Nv21M2/m2HO0wmqZGprS1teW3\n73zL0zjNeyvLJ+h59+5dLp05k5s2bqS/vz9zi8hlKEkSt20Tl2nQILHuVhYs/HthgdPMg8yyJ6b9\n/wlVRFgx/CvX7cEDsmtXUY4f/z9FgPkoLxGWpCxTH0ADAMsBfAYhYQEIEe4gkvoiG/6DqJJYe06E\nhQHvvCO2Tk6CCsPDkaa8juDgvrC0bI127c7DyEjIXZFEhm8GIj6KQHZoNmpPrY1GPzSCylIFmcTg\nkBCcTU1Fmy2uCN5rjRMngL59C+9SZ9AhS5uFbF02srXZz2yNlEbo06gPLIyLl2YiiRH7R+Bw+GE0\n9GyISCkSPdADX/X6CsZ+xrDrbYc2x9sUq+tYUfzxBzB6NPD668Cffwot0NKwI3AHxh8dj4muE7F5\n8ObK15CsQhWq8AzKK7FmVNwXJKMBRAPoWhkHVoX/GLZvB6ZNA6ysgPHjhcDkgQPIMolBSMAgmJrW\nR5s2J6GEJVLVqUg+nIzkI8nQ3NPApKYJ2vzVBg4DHAq6W37vHv5KSUFbqQmu/W6N338vTII6gw4/\nXvwRS7yWIE+fV+KhWZtaY3Sb0ZjYYSI61OrwzPfLLyzHwfCDUJ5TIiMiA/v27kPX+10R9XkUjO2M\n0Xx780onwYMHhVZoz57AkSNlI0GvaC9MOjYJvRv0xk9v/FRFglWown8UZck+0Q3AOgAtAJhC5ArM\nImn94g+vZFTNCCuAhw+hHjUKbmfOCCHbxYsFYw0ahNxd3yMg4GUARnBJPYaMQ2Z4+OdD6JJ1UJgq\nYN/PHo5DHeH4liOMbR8LNp9PTUWfoCBUu+KE9PktsG6tAjOfkEcPehCECX9OwLX4axjafCh61e8F\nC2MLWJpYwtLYstA2OScZ2wO3Y3/YfuTp8+Ba0xUTO0zEqDajYGtmC4/jHpjlPwsIB8aYj8HqVavh\n4CAIOfduLhRKBczqlYGlyoFDh4CRI4FmzdTw9XVDtWqlt4lMiUSXX7qgukV1+H7oCztzu0o9pv9r\nUKvVBRqRVSg7qq5bxVBpM8InsB7AuwD2AegEYCyAZhU7vCr8KzAYgLNngW3bIB89ClmrxbFRH+FS\nn8mwXe8Pmw4rYG3fFI6n3KA0yYFingcibqRBZa2CwyAHOA51hH1/exhZPTtc4jQaDL0WBt63gNHa\npjh9SlEwE9QatPjW61ss814GB3MHHBhxAMNaDiv1cHs36I11A9bhl0u/YPOVzZj+13TMOjELDg8c\nkGidCCOtEfaM3YNhgwr3Ze5S+el5jhwRJPjSS8DChSgTCabkpuCN3W9AAQVOjDrxP0+CVajCfx1l\nmRFeJdlRoVAEk2z76LNAks/msPmHUTUjLAWRkcIEun07cP8+6OAAdYPXYX61H/LY4HE98xzIa+YA\n9aNxa+Mq3GBL1BlaHTPfbQZTs+LflTKyZTQ9EYSEapn4f+3dd1xV5R/A8c/DRgRRRBRFRXHh3iMt\nU3OWmZmj7Oco08htrtRCrSz3KjO0LCv3yMyBEriw3HsPFBkKyN5wv78/LjnKATdRkef9ep1X95x7\nzj3P+VZ+Pc+ss6guG+baUbKk8bv9Ifvpu6EvJ26c4O0abzOrzSycCjjd97cArl27xvz58zl27BjH\njx/n2rVrxi9KgGVDSwxVDZhbmLOn9x7qla3332KTDRs2wOuvg2fNZDwGe7Hl2kpervgyA+sPpGnp\npves6kzLTKPtT23ZfXU3fv/zo1mZZrleTk3T7pYbb4SJSilr4KhSaioQzu2OM9rTRsS4DpiPD+zY\nAWZm0LYtzJnDaptqOHYKI+a5AtR6rQDW4/pj0dCNC9MjiE24iFvl1ZT+pTUHg4MZGRbGypMp/FKl\nCh73WFPs3DlouvQyES1j6XisCmtW2GFhAcnpyUzcMZFpgdMoUbAEG3tspEPFDg8t9qZNm+je/TsS\nEjpTrlwoL7zwAtWrV6datWpUr14dNzc3kjOSSUxLxNnOOTcid5eNG6FLF6GQ+0WOvVSPSyGZdKzU\nkS0XtrDy5EpquNRgYP2BvFn9Teys7ABjJx6v373wD/Lnx04/6iSoaXnFw7qVYlwKyRYoBHgDMwGP\nnHRNza0NPXzi32bONPbv9/AQ+fxz4+wvIhIfmyo/lw6Q9c4BsnXtVpGXXhKDvZ2c3PeK+PsjYWFL\n7vqZ1TduSOFdu6Tgzp2yJCzsrgHfy5eL2LSMEPz9pf2224MEdwTtkIrzKgreSL8N/e6a8ut+0tLS\nZPjw8QJzBUTMzAy3hiccPfqIYiLGacr+DP5TjoYflaS0pAee67MsVMws0gTXfWI7voSM8h0lEYkR\n4u/vL4lpieJz0EdqLqgpeCOOXzjK8C3D5ULUBfly95eCNzLeb/yjK/gzQg+fMI2Om2nQk27nY2fP\nGifqfPnlf439Wd59v/gpfwnYcFX8R40SA8i51c3F3z9r/tB7uJqcLC8cOiT4+0v3kyclOi1Nxo4V\noUSSmG/aKdUD90tyRoZEJ0dLvw39BG/Efba7+F7wzVZxg4ODpWbNvgKnBEQGDkyXyEhj/nZ0NE6v\n1qPH3csNZldYfJisPbVWRmwdIY0XNRaryVa3JqdW3krKzi4rbZa2kSGbh8jX+76WPy79IUfCjkib\nj2cL5imiXA+I16pxd437u/MPJYPBILuv7Jbuq7uLxSSLW8smdV3V9dY8otpt+g900+i4mSanifBB\n4wiPP/hF0the+CTpNsI7ZGZCs2Zw5gycOAGurre+OrcslNA3z7H/XVtGTioNnp5cfd+RS62DKFVq\nGOXLz7hv1/5MEb64epVPLl/GGWvCR1SmyEcXMRRL4WDdOhwK2sSgzYO4kXiD4Y2G493c+1ZV4YNs\n3LiFrl0Pkpw8isKF01m5sgCtWt3+Pjoapk6FOXMgPR3eeQcmTOBWG+S9+F3yY8nRJQQGB3Ip+hIA\n1ubW1HOtRxO3JjQq1Yj0zHTORp3lTOQZzkad5WzkWRLTE40/cL4NrFiPc5kIAvws8SxT/OFxB8Li\nw1h4cCHBscHMbz8fW8tH32lH07Tsy2kb4YMSYdkHXSgiQTkpWG7QifAO06fDyJGwdCn07HnrcMrV\nFHZW/4uLJYUW26pQqWN7wkod5+ywdIoVe5MqVZailNlDf35PdCwt/jhFmlMqAN+VLcL6Pyew4ewG\nahevzaKOi+455u+fMjIyGDhwFgsXNgGeo337OJYudaBIkXufHxYGn30G334L5ubG8f9Fi4KdnXEI\npJ2dcTsbe5CpB7wpXOo6zWuXpolbE5q4NaF28dpYW1jftzwiwvY/rzN9hgG/X12oXCWTnQFW9y2P\npmlPv0eWCP/xoy5AA4zzMO4TkRumF/HR0Ykwy5kzUKuWsVPMunUkpwSRmnqNtJTrnPniEClx1wl7\nM4X6p7eTnhaBvxm82OIlqlf/DTMzq4f+fERiBO8t9GF9+PdQox1E7cE6/iRmyoxJL05iaKOhWJg9\nuN9VWhocORLFm28u4eLF97CyMmfhQgt69374/QEuXwZvb9iyBRISICnp/uc2aAA9ehiHPZQoce9z\nRGD7duPfH3x9wdYW+vSByZO5bxLUY7pMp2NnGh030zzyXqNKqa7ANGBH1qH5SqmRIrLKxDJqj1Jm\npnFmGDs7MubP4MLZfoSHL779fSewAtxTLYgrkoGVswdFwitQterKhybBQ2GHmLdvHsuOLyM1M5VC\nKS0pn7iHQzGHSAWauDWhZ42edyXBU6fgzz8hKOj2dvkyhIQIIk7ACDw9w9m8uTilS2f/Md3d4Ycf\nbu8bDJCcDLsuHOL1n3pR3Ko881st4cQBR375BYYNgxEjjHMG9OhhHAZRuLAxIS9bBjNnwrFj4OIC\nn34KAwaA04NHd2ia9ozKzjjCY0Crv98ClVLOGCfd1m2ET4OpU2H0aJIWT+J41R9JTr6Im9sILEMa\nc/Hdm+ysVgiHRucYNno8zJ8PH3zwwJ9Lz0xnzek1zNs3j8DgQOws7SgX14sT3w/k3dm/4HPuU2a2\nnklBq4IM2TIEB2sHfur8E63KtWLvXmMzZWamcdRGqVLGBFa4cAx+ft+RkXGBqVP74+VVE7N71MZe\nir7E0qNLebfOu5R0eEBjYJYTN07w/PfP42jjyO6+u3G1v90ueuaMMeH98otxOKWlpXGO0KNHITQU\nqlaF4cONc4da37/mVNO0PCinb4TZ6Zl5nKyEmbVvBhzPSY+c3Np4RnuNRkX9axH3W84mJsrYixdl\n9Y0bknnihBisrCShraf4/2EmgYFuEh0dIGk30ySwdKCsLBkgnis3SoqlpcikSQ+9r8FgkNdXvC54\nIx5zPWTW3lmy+0CMmJmJvDx0s+CN9Fnf59b5x68fF8+vPEV5Kxm+frKULm0Qd3dj59W0NOM5f/31\nlzg5OYmLi4scOXLkvvc+HHZYXKa5GNcW/NRWJvwxQeJT7798+vmo81J8enFxneEqF29efMAziezf\nLzJ8uHGJxVatRDZvzpMT6mualk3kwnqE0wBfoDfQB9gCTM3JTXJrexYTYUiISLFiIiVKGMfr/f0H\n9smEBHnz5Ekx8/cX/P3FfPt2OeVZQVILWcjuNcjJk90lJSVafvjBIDWKJEpF4sS2fIxUczwg7cue\nkNdeM0iPHiK9e4v06OEvQUH/vvfy48sFb+QT/08k05ApBoPI88+LOJa5KkW+cJLqX1eXxLS7M3RC\naoL0WddXqLxGlHm6bPjj9nCDbdu2iZ2dnbi7u8uFCxfu+8wBlwPEYYqDuM10E98LvtJ9dXfBGyk+\nvbgsOrhIMjLvXk02ODZYyswqI05fOsnJGydND3YO6a7sptOxM42Om2lyIxF+iHF+0ZlZ22s5uUFu\nbs9aIkxPNyYeOzvjYtAg0qhFurT5/Zwof3+x27FDRl24IKEpKXJ8eEcRkAMfW0vvwIkycX2U1KqY\nLiBSjnhxKxUhhSpeleecz0q9egapXl2kQgWR0qVFzM39xdJSpH9/uZUQbyTcEOepzlL/2/qSnrUI\n77JlIpinivtnjcT+c3s5G3nvFXa/+spYVqt2Y6TIl0XkxyM/yoqVK8TKykqqV68uoaGh933mdafX\nifVka6kyv4oExwbfOr43eK80XtRY8EZqLKhxa2zijYQbUnl+ZXGY4iAHQg48oshnj/5DyXQ6dqbR\ncTNNbiRCb+AksBsYBLjk5Aa5uT1riXDcOOO/kaVLRf68GSvVxoQIdumCVaY0GxIlwbGpkpmZKhd/\nfVkyLZCbLZ1kzq6jUrxOpICIM8kyxvGMzPPaLMrPX/587717LqF+9aqIl5eIlZXcSogdFwwSy0mW\ncvz6cRERiY8XKVlSpNjbQwVvZOWJlfcs8+HDItbWIu3bi5y+cVbqf1tfeBlBIZ51PSUqKuq+z7v4\n0GIxm2gmDX0aSmRi5L++NxgMsvLESnGf7S54I+1+aie1v6kttp/ays6gnaYFWdO0Z15OE2G2hk9k\nNT7WBLoCXYBrItIy2w2RueRZ6izj62sc/dCzt4Gk4adYExmJo4UF71qV4dKMkqxdaUaDstf5stUQ\n6m9fgXWsHR83+IvpvlUwF6G71WUsup3nh562pFtB9+PHWdav3wMXzgsOhi++gG99MsnIzKReh2Os\nnlePMmXgo49gyvq10O11BjUYxNx2cwHw8/Pj+HHjXAupqZbMmNGDtDQrPvzwZwoWTObixYvMnz8f\nW09bkjsl06JSC6a2mkpd17q37isiTN0zlTF+Y2hTvg1ruq554CD81IxU5u+bz+Sdk0lKT2JDjw20\n9Wj7iCKvadqz5pF3lpHbb18lML4RBgLHcpJtc2vjGXkjDAkRcXYWqeCZKeUC9ollQIBMunxZYhMT\nRfz9RcaMkViPrLpSkGizQtKVNaIwSDuuyD7elwx7Z8moW1eWffSRdFm5Uq5GRNz3fndWt0QnR0ux\n8XXF6fllYmVlEEtLke7dRSyKnRfLjx2kgU8DSc1IleDgYOncubNgHEuatS0RyBB44a7j//vf/yQ+\nKV5m750tTl86Cd5I99Xd5eLNi5JpyJQRW0cI3kiP1T0kNSM123GKSoqSMxFn/kOk/xtdTWU6HTvT\n6LiZhlyoGvUCAoBTwETAMyc3yM3tWUiE6ekiL7wgYl3AILY/7BOX3bvl5PLlxvlC7eyM/4osLCS5\nYTk519tcPm8wVqxJk5rqpvz2or+kbw8UiYjIUTfIO//n6ru+r5hPNJcDIQckONhYZYplktC/llhN\nKCyBpy7IrFmzpGDBgmJraytTpkyRqKgoWbAgQUBk9OhkiY6OvrXFxsbeda+Y5BgZ5zdObD+1FctJ\nltLQp6HgjQzaNCjPzcmp/1AynY6daXTcTJPTRJidcYRTgBUiciTbr5mPybNQNTpuvPD5ZwrGnKZh\nlyTWFyhA8Zo1jVOivPwytG7NjaoRnLrWD/uwpsT3nICDaxLVDrfHqmj2ZmURMQ509/U1bseOGacl\no7wv5xu1oUL4WBomfI6DA2RkwLdh70FdH8yWbUDOvYTIfFq2PISPz2e4u7tz9izUrQv16oGfn3Hq\ns4cJjQ9lYsBEvj/yPROen8D458ffd35TTdO0/yJXplh7WuX1RLhucwadO5hD23DenRXH/AoVsO7Z\n07gs+oUL4OrKzZvbOH68A7YJdUh6zZtClsFUv/IWFkX/vUbg36KSoshMKIKfn7qV/EJDjd9VqmSc\ngiwxI55NZauhMgpQftthEmNtiE1MJsZzBobmE6idUIfD02OwtZ1CSsobFCgAgwYpBg2C9u0hJASO\nHHnwJNj3kp6ZjqW55X+ImqZp2oPlWhvh07iRh6tG/zifKOaF04SyCTLnfIhxvb8DB4xVoePGiYhI\nXNwB2bmzoARu8RR/uw1ymBmSseOv+/7mpagrUm9aJ+NyQ/1rCzWWSuGiqdK1q8iiRSJXrhjP8/f3\nF6+NXqK8lQReDZTk9GSZ99c8KTG9hOCNWPeyFmWuZPDgwRIbGytnzhjbDZUSMTMzFnHjxscRpaeL\nrqYynY6daXTcTEMOq0azs0K99ohtuB7Fa2+YY0i25qctBt7ycDXWX44ebVxaYdQokpIucOxYO1Ry\nYVLfnEThxNNUGxaN+fMN/vV7aRnpvLt4Fj9dm4gYwOnKYMwqbCOi89vYFBxFzQYD6VS3P04FjJNp\nHgk/wtdnv2ZQg0EcDj/MG6veICQ+hOoO1Yn4KYKKthX5/q/vqVvX2NPTwcE4Xdm4cTBlCtSoAR0e\nvui8pmlanqCrRh+j8HCYsSaR6X9Ew9pSDPoonbmfZVUTbt1qHD8xZw5pA7px6FAT0hJiMPSZjVNk\nJJ5uizE/duCu4RAiMG3lTj7Z9z4pDqcoeO1Vvmg+h/d7lAFlwPeiLzP3zmTbpW3YWtjSq2Yv+tfr\nT5eVXYhNjcXGwoZrcddoWropXZ27MrrbaDzKexAQEEARvQ6Rpml5lG4jfMokJ8OGDfDjj7B5RwbS\nIAr8XSjglElSlDm9e8PULww4t6kD8fEYTh7j8MkWJMQcRwZNp2iqA56X+mK2JwCaNAGMCXDNlhu8\nv24UkSV/wCKhDAPLz2Pau69gcY93/BM3TjD7z9n8ePRH0g3pt443LtWYic0nUjSuKC1atKBo0aLs\n2rWL4sWztyCtpmna0yinifDhK7JqOSYCu3fDe+8ZO3927w5HjgoFaySCvws9hqRwPcicMWPgp59g\nQrmf4ehRDJM/I/j6bOLj9yGTR1GshCeel3qjhnoRXbsKAadPMGSuL+V6TueNHZWJLP4Lbe3GEjnx\nFLMG3DsJAigU1+KukW5Ip4htETwTPNny1hb29N1D6YzStGnTBnt7e7Zv366T4AMEBAQ86SLkWTp2\nptFxezx0G2EumD4dRo0yDlF4/XXjArEfTk8h1L8Q7cZG88vnhQFje9v/uqZQuPF4DlCXycs8Gejy\nNut2ludynb0kpHxJaC1FsMNC0qfOuX2DiuBh0ZxVvb6mVqkq9y1HZFIkn/h/wsKDCyloVZCZrWfy\nQYMPCNwVSHOP5ly5coVWrVqhlGL79u2UKVMmt0OjaZr21MnVqlGlVFtgNmAOLBKRL//xfWXge6A2\nME5EZtzxXRAQB2QC6SLyr14iT2PVaHIylCkDNWvCunXGcXnPt8vg+F/m1JwQwmHvknePn5sxAz78\nkO1jfQkoNZif488RlGLALdGR8jdiOBXfkhvxtXGxc6VpTVcaVBF2b/qFQlKIalWr4enpiaenJ+7u\n7phlLfKXlpnG/H3zmbRjEglpCQyoNwDv5t4ULVD01m3Dw8Np1qwZkZGRBAQEULNmzccdKk3TtFzx\n1AyfwJj8LgBlAUvgCFDlH+c4A/WAT4ER//juMlDkIfd4FD1tHykfH+PwAj8/kbAwkao1MgWLTHH5\n9KxEZy3Sd/nyZdm3b5/IzZsihQtLeuuX5J2Vz4mZN1J0rL00qzhFMlGyoqiXfPqpyOnTxgmofXx8\nxM7OTuzt7aVkyZJ3TWtma2srtWvXlk5dO4nTy05CV+S5z5+TA0H/XqEhKipKqlWrJnZ2dhIYGPi4\nQ6RpmpareNRTrJm6AY2BLXfsjwHG3OfcT+6TCJ0eco9HHL7/JjNTpEoVkVq1RC5eFClf3iBmNhli\nOf2YHI6LExGRc+fOSbFixQSQFWXLikEpaTuymOCNdPQuIUeGBEqaWzlJK1lGJOua8PBweeWVVwSQ\nFi1ayNWrV0VEJDo6WgIDA8XHx0eGDRsmrV5qJZaFLf8xHyhSqlQpefHFF6V///4yffp0qVy5slhZ\nWcn27dufVKjyJD2my3Q6dqbRcTNNThNhbrYRlgSC79i/BjTMwfUCbFdKZQILRcTnURYuN2zdCqdP\nw+TJ0KwZ3Ew0YJh+lEWdS1DL3p7Q0FBat26NwWDg0yH96ThvIT/WgB0qklEFbXl97SKqpw7HLDLM\nOHeZvT2//vor/fr1Iy4ujlmzZjF48OBbVaCOjo40btyYxo0bAzB0y1C2/7Wdnzv8TGWzypw7d47z\n589z/vx5zp07x6pVq7h58yZmZmasW7eOli2f+AIimqZpT15OsmZONuB1wOeO/Z7AvPuce683whJy\nu/r0CNDsHtc96r9I/CctW4o4OBjX+StSPENYvE/ePWNcLeFWdaSDnXiv85Zl9Wwl2QJ52auUFCiE\nKJAuRcvKWaVEfv1V4uLi5J133hFAateuLSdOnHjgvdeeWit4I4M3DX7geZGRkRLxgJUpNE3T8jqe\nojfCEMDtjn03jG+F2SIiYVn/jFBKrQMaALv+eV7v3r0pW7YsYHxDqlWrFs2bNwdudz1+HPvbtoGf\nn3G/VYdm7Ou/H4/Qo7xxzYPEUqVo92o7TnEKh24OrPb15uhBWNOuCS099tPv/YZsXVKAxeH+rAHe\nWrWKPUOHEhQUxFtvvcV3332HlZXVfe9ftlZZ+m7oS8W4inSwuj3ly+N8fr2v9/W+3n9S+wEBASxZ\nsgTgVj7IkZxkzZxsGIdmXMTYWcaKe3SWueNcb+54IwQKAPZZn+2APUDre1z36P8qYYJ164yrtIPI\n9BkGef7gISm0c6dcTEqSK1FXpFy/csJoBG9k1NBqkljKRQyOjnJoS13x32Av+6suFgNmEj5ypAwd\nOlSsra2lXLlysnv37ofeOzUjVRr4NBCHKQ5y8ebFbJVXtzuYRsfNdDp2ptFxMw1PyxuhiGQopQYC\nWzH2IF0sIqeVUv2zvl+olCoO7AccAINSagjgCRQD1mYNM7AAfhYR39wqq6kSE2HYMPDJar186y0o\n1D2MnedimVzMnC+2D2HxgcUYXA20T6nK0kAnivjuhMqVuT67FbHW81Gzx1D15ATUe+/i8uWXzFKK\n8ePHU6BAAWxtbR9ahrHbx7IvZB+r3lhFucLlcvmJNU3Tnj16ijUTnDlzhp49Z3Px4kRiY4tRt24y\nBw4UYM+ZFFqf/RabsHXcDN+BmZhhvi+TtekNaL/nGChFxtiBJL7XjqMn2iF761JhfBFKvmoOq1dz\n36lh7uO3s7/RcXlHvOp58VWHr3LpaTVN0/IWPdfoY9Cw4Wj27fsUpa4j0hPMd2BT3xVD8yTSbGJw\nsLSibEQazt/Aj5bgGg8Rz8MFL0h1yfqR+II49h1CzQr+KL/tkI23vztdjb1KrW9qUdaxLIHvBGJj\nYfPwizRN0/KBnCZCPcVaDvn6BrBvX2+KFI5n544Exvi4cjbRFnuLUOxPg/1xsA9K41UDdAMyXIoS\n+XV30lvUoHhwBjF/xBG3Kw6zY6Wp4rgEtfH3HCfB9Mx0uq/uToYhg5VvrMxxEgwICLjV4Kxln46b\n6XTsTKPj9njoRJhdsbEYdu7k4puz+VPFUjf2EBY1r0IN9gAAEUBJREFUhN/uc3q6hQWZ48ahho4k\nY0M84a+HEvdnHGbWgov44VZoEdaBa+AByx2JCCkZKcSnxROXGkd8ajzxafEsO76Mvdf2svz15XgU\n8cid59U0TcsndNXo/URHw86dsGOHcTtyBAwG0rDkSNFi7KgYgpNzYw76taSt1w7K2u/C4FSJyjVm\nYF3Ug6QkB0J/TiT8+3AybmZgW8mWkrWDcVnVD8tKrrBxI7i737qdQQwcDD3IhrMb2Hh+I0ExQcSn\nxpMpmfcs3oC6A1jw8oLceXZN07Q8TLcRPgqnT0PDhhAfD9bW0KgRmU2b0nGGLf6p7+H4ZV2qFq+E\n5bIf6di9M5VL/8llu7fpVXcRSSfSCPIOInJdJJiD82vOuPYvjqPvVNS0qdC6NaxcCYUKkZyejN9l\nP2PyO7eRsIQwzJQZTUs3pUaxGjhYO2BvbY+9lT321vbGfSt7CtsWpnbx2ndP3q1pmqYBuo3wvxMB\nLy9jD05/f2jUCGxsGDpoLZtSOvP8e9+wMymYwQ79qfBOHeyKxLDQ0pu5VsM43e08EasjMHcwp8z4\nMri+74p1oQx4+23jUhTvvw9z57Ltij9fbf4K34u+JGckY29lT1uPtnSs1JF2Hu1wKuCUq4+o2x1M\no+NmOh070+i4PR46Ef7TL79AQADpn81DqjXBysaKyMhYFizwxMYmFLOGS3GJLEDdgh9zPak0M8K+\nZvKaWpxcdwjzgsYEWGp4KSwLW0JICDzf0VitOmcO6V4DGOf/EdMCp1HSviR9a/elY6WOvFDmBawt\nrJ/0k2uapuVLumr0TjExUKkSmc5u7Do1FcQMiyIWDM8IYX9cN/73zjv86PYdfcpY4Hq+F+ZHOtF8\nc0HMC5hRanAp3Ea4YelkafytQ4fglVcgLg6WL+dq0+p0X92dvdf2MqDuAGa2mYmtZc56i2qapmkP\np6tG/4vx45HISM6VmImlszVuo0ux59wG9i/sjZPTRpLr/IT5DUWHcQtxCi1Hig04D3el4uiyWDlb\n3f6dzZuhSxdwcoI9e9hgHUTvb2qRYchgRZcVdK3a9Yk9oqZpmnY3syddgKfGwYPw9dckt+7D9aOu\nOM05QHjTdnz4mxNgyaz5p9kWV4Di1zqxoGYd5g6C6P0VqDa94t1JcNMm6NQJKlUibe9uhoct4dXl\nr+Je2J1D/Q89FUnw78lqtZzRcTOdjp1pdNweD/1GCJCZCQMGIC4unDjfCfPpXxBe3Jc/Nr5NaOib\nNGiwhRSPosScjSHG/nVCRsXwoZsb3cu53v07mzbBa69BtWpcWb2YNzZ1YX/ofgY1GMS0l6bpdkBN\n07SnkG4jBFiwALy8uN5zEqeb/gQVz1PK7Qvq1OlGQgJcumRH3YXtuGkRAy2+ZZibGzPKl797+MKm\nTchrr5FQsSyzJ3dgxpnvAPju1e/oXKXzfy+jpmmali16HGFOXb9urMas6kHgiEsouzSq1l3OxIlV\nmD+/PG+9tZoMl9KscGgIHoMZ1GAgczw8/g4052+e58zSWbQb+S0nikHLngbi7MxpWa4l33T4BvfC\n7g8vg6ZpmvbI5DQR6jbCkSORpAQO9zsKybZUK7WDw4fbs2BBcayt/Snv0Y4V5lPBzIa+tXoxx8OD\nmJQYvH73wn2OO0OGVKLNh99wrrgFP8/oxfd91hM1KoqtPbc+tUlQtzuYRsfNdDp2ptFxezzydRuh\nwf8PzJYu5WpPSI6qQ7HQb5h7rg6TJglwlc6dI5l09Sy4/0YV9874eBpncxnhO4Klx5bycVIDxq4K\nIbNqRar672L6A+YN1TRN055O+bZqND3xBpk1yiHJiRz9oAvhs4Yxp0ojAnabAT/Qps0Jthbzgpem\nwaUFHO5/hFrFa7L76m6afd+M76y60mfir+DpCdu3P3DybE3TNO3x0W2E2ZCZmULoEHfcvgonxPsd\nlnsP5Ev76sSmCmlp79K6bTJ+JaaQ+XYQBQ/2oVaR0uzqu4sMQwZ1Ftah5tFwflwSh9JJUNM07amj\n2wizIcxvOK4+4aS0acgnc70ZSU2sCyWRnlGH4o3Psf3998j831WeS71IQuJVvOp7ATDvr3m47D3O\nku9jUFWq5NkkqNsdTKPjZjodO9PouD0e+S4RJt48iqPXAjIL2NLl7HIW3yyFe9VLXLtRBvFIJWaM\nN4ZAVz68WQ2nmN8pZleMzlU6ExIXgt+ij9i43Ayzynk3CWqapml3y1dVoyIGIt4uTbGfQ3jDYS0b\n4jryoutefBM6YO/oyCc/bOWjVyrS+kUz5v14lXJz3Rnz3Bg+a/kZk7xf5MPPA7DwqIjVjt3g7Jx7\nD6ZpmqaZTFeNPsDN5R9S7OcQFtr04/fUDkzGj0MZ3Shma8tBP39+/aQyNuZmLFgAPoe+BeC9uu9x\n4JcZjPg8gISSzlgF7NJJUNM07RmSbxJhWsgpbN+fzynzyoywnMrUtN34FP6AlOR4tmzZgq9vOXbu\nhBkzwKFoPD6HfHi54suUOHKBKn1GElbEEofd+6FYsSf9KP+ZbncwjY6b6XTsTKPj9njkj0QoQkSn\nVzCLNeOtAj8wxfkE31gM5mriVX799VcKF67F6NHQqhX0eDuZjss7EpUUxUj7tkj79gTbC8HrfsCm\nZJkn/SSapmnaI5Yv2ggPDBlCvblzGVlgCi6vNmX2su5EWkaybMUyOnV6jbZtYc8eOHwsnWF/vsam\n85v4qfondO81nYvWiUz7rD3f9t/4GJ5I0zRN+6/0eoT/sG7pTtrO/Zbtli9SeFQNJnm3x8LKgj/8\n/6BJkyYsWQK+vjBnbiYTDr3N7+d/55vyQ3mzz0zC7Ay072WDf49vnvRjaJqmabnkma4anesbSvne\nH5Cg7Njt1ZhPJr5KEbMiBO4KpEmTJoSGwrBh8FxT4ViZAaw4uYKpjm/Qv8984lwcqf9mEv1fnUQp\nh1JP+lEeKd3uYBodN9Pp2JlGx+3xeGYT4WS/CAyvTKGG4QSLmpVj4pzPqS7V2fLVFio3qIwIeHlB\ncopQ4YMRLD68iHGZzzFy6CrimtSjSR8Djh5VGdJwyJN+FE3TNC0XPZNthNsuxTOjtj9b4l5lZfHC\ndAuPpoNFBya2mEidLXVQSrFiBXTvDi99NpFt6d4Miq7InDnn2PFSBVo3Oo9DQSc2vrmRRqUaPYEn\n0zRN00yV7+cajUnLoEmDE+w62pJIyyRqpqcwoMIQOod2psHJBtiUseHAAXjpJbBvPYtgz+H0CnHm\nu0URfPySBdOaKoY0GspHzT7C0cbxCT2ZpmmaZqp8PaBeROgw5Aqrjr6FUom8plKZ98G3dDrfifJf\nlsemjA1790LLlmBefxHBnsPpeNma+Usi6NYFLvR7nTMDzzL1panPdBLU7Q6m0XEznY6daXTcHo9n\nqtfoR6sj+OibQVTkLB3MM5n1y1rs+jlj19QO1/dd2bkT2rUXbFt9SVTtsbS8DF+tTWX4h9UY4eWj\nq0E1TdPyoWemanT3pUT2eX7E8NS5fGBmTbtfv8P9h5pE/hZJ/aP1CQwuwCuvZmDXpRdR5X6h+3GY\nsMeCoO9m0q7tQJTK9lu0pmma9hTLl+MIE9MyWdZiEV+lzmU+TrywbBINEltxavUp3Ke4s+NSATp1\ni8e5Vy1CXC4xdhd0tK1FueOb8Sxa/EkXX9M0TXuCcrWNUCnVVil1Ril1Xik1+h7fV1ZK7VVKpSil\nRuTk2jsN67aeWVdGsg1XrKd5UW1Dc051P0XBugU5UsGNd9/dRsneToQ7X2LyTgt6D/6eRr8dxiaf\nJkHd7mAaHTfT6diZRsft8ci1RKiUMgfmA20BT6CHUqrKP06LAgYB0024FoBZ8/7is/UDuIwThzu1\noNLHrYhYHUHpsaUJ+qAayya+hlm31kQUTOezm7UZvTGGih17P9qHzWOOHDnypIuQJ+m4mU7HzjQ6\nbo9Hbr4RNgAuiEiQiKQDy4FX7zxBRCJE5ACQntNr/9ZqSB8sSGOZRzUarH8Hh3ZOyMzSbLyyhbA5\nRdncYQOploqfX5zP6HmHsLS1e/RPmsfExMQ86SLkSTpuptOxM42O2+ORm22EJYHgO/avAQ0f9bVV\n5BwT3OtTXJ5jT70PKBh8mvSfhWAH+LojlDRzJGDwIcoWcTfpITRN07RnW24mwv/SHTXb1w5tl8lX\nDf8E/rzruAXmtCj9Ait7rKWQTaH/UJRnT1BQ0JMuQp6k42Y6HTvT6Lg9Hrk2fEIp1QjwFpG2Wftj\nAYOIfHmPcz8BEkRkRk6uVUrl3bEfmqZpWq55WoZPHAAqKKXKAqFAN6DHfc79Z4GzdW1OHlTTNE3T\n7iXXEqGIZCilBgJbAXNgsYicVkr1z/p+oVKqOLAfcAAMSqkhgKeIJNzr2twqq6ZpmpZ/5emZZTRN\n0zTtv8qzk27nZMB9fqaU+k4pdV0pdfyOY0WUUtuUUueUUr5KqWd3hnETKaXclFL+SqmTSqkTSqnB\nWcd17B5AKWWjlPpLKXVEKXVKKTUl67iOWzYopcyVUoeVUr9l7eu4PYRSKkgpdSwrbvuyjuUobnky\nEeZkwL3G9xjjdKcxwDYRqQj4Ze1rd0sHholIVaAR8EHWf2M6dg8gIinAiyJSC6gBvKiUaoqOW3YN\nAU5xu+e8jtvDCdBcRGqLSIOsYzmKW55MhORgwH1+JyK7gOh/HO4I/JD1+Qeg02MtVB4gIuEiciTr\ncwJwGuP4Vh27hxCRpKyPVhjb+KPRcXsopVQpoD2wiNsdCHXcsuefHSdzFLe8mgjvNeC+5BMqS17k\nIiLXsz5fB1yeZGGedlm9l2sDf6Fj91BKKTOl1BGM8fEXkZPouGXHLGAkYLjjmI7bwwmwXSl1QCnV\nL+tYjuKWV1ef0D18HhERET0e8/6UUgWBNcAQEYm/c7kuHbt7ExEDUEspVQjYqpR68R/f67j9g1Lq\nZeCGiBxWSjW/1zk6bvf1nIiEKaWcgW1KqTN3fpmduOXVN8IQwO2OfTeMb4Va9lzPGrqCUqoEcOMJ\nl+eppJSyxJgEl4rI+qzDOnbZJCKxwO9AXXTcHqYJ0FEpdRlYBrRQSi1Fx+2hRCQs658RwDqMTWc5\nilteTYS3BtwrpawwDrjf8ITLlJdsAHplfe4FrH/AufmSMr76LQZOicjsO77SsXsApVTRv3voKaVs\ngZeAw+i4PZCIfCQibiLiDnQH/hCRt9FxeyClVAGllH3WZzugNXCcHMYtz44jVEq1A2Zze8D9lCdc\npKeSUmoZ8AJQFGNd+cfAr8BKoDQQBHQVET3N/R2yejruBI5xuyp+LLAPHbv7UkpVx9g5wSxrWyoi\n05RSRdBxyxal1AvACBHpqOP2YEopd4xvgWBs6vtZRKbkNG55NhFqmqZp2qOQV6tGNU3TNO2R0IlQ\n0zRNy9d0ItQ0TdPyNZ0INU3TtHxNJ0JN0zQtX9OJUNM0TcvXdCLUtKeYUqqQUur9rM8llFKrnnSZ\nNO1Zo8cRatpTLGvC799EpPoTLoqmPbPy6qTbmpZffAGUV0odBs4DVUSkulKqN8alZQoAFYAZgA3w\nJpAKtBeRaKVUeYxrdzoDSUA/ETn7+B9D055eumpU055uo4GLIlIb4xI9d6oKvAbUBz4D4kSkDrAX\n+F/WOd8Cg0SkXtb1Xz+WUmtaHqLfCDXt6abu8xmMa/0lAolKqRjgt6zjx4EaWZMQNwFW3bF8lFVu\nFlbT8iKdCDUt70q947Phjn0Dxv+3zYDorLdJTdPuQ1eNatrTLR6wz+E1CkBE4oHLSqkuYFxaSilV\n4xGXT9PyPJ0INe0pJiJRwB6l1HFgKreXhJI7PnOPz3/vvwW8o5Q6ApwAOuZuiTUt79HDJzRN07R8\nTb8RapqmafmaToSapmlavqYToaZpmpav6USoaZqm5Ws6EWqapmn5mk6EmqZpWr6mE6GmaZqWr+lE\nqGmapuVr/wfTdotP9JT+FgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e107db90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(7, 6))\n",
    "ax1.plot(S[:, :10], lw=1.5)\n",
    "ax1.set_ylabel('index level')\n",
    "ax1.grid(True)\n",
    "ax2.plot(v[:, :10], lw=1.5)\n",
    "ax2.set_xlabel('time')\n",
    "ax2.set_ylabel('volatility')\n",
    "ax2.grid(True)\n",
    "# tag: sv_paths\n",
    "# title: Simulated stochastic volatility model paths\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "uuid": "398e803e-e0d8-4bc1-9c2a-53ad78cf524d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         20.136          0.176\n",
      "           max        520.205          0.319\n",
      "          mean        108.326          0.243\n",
      "           std         52.848          0.020\n",
      "          skew          1.756          0.178\n",
      "      kurtosis          5.536         -0.006\n"
     ]
    }
   ],
   "source": [
    "print_statistics(S[-1], v[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Jump-Diffusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "uuid": "4d34dbf3-196e-4125-a11d-f967982540e2"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "sigma = 0.2\n",
    "lamb = 0.75\n",
    "mu = -0.6\n",
    "delta = 0.25\n",
    "T = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "uuid": "b22527e8-afc1-4c69-8253-4e8b6a64f0da"
   },
   "outputs": [],
   "source": [
    "M = 50\n",
    "I = 10000\n",
    "dt = T / M\n",
    "rj = lamb * (np.exp(mu + 0.5 * delta ** 2) - 1)\n",
    "S = np.zeros((M + 1, I))\n",
    "S[0] = S0\n",
    "sn1 = npr.standard_normal((M + 1, I))\n",
    "sn2 = npr.standard_normal((M + 1, I))\n",
    "poi = npr.poisson(lamb * dt, (M + 1, I))\n",
    "for t in range(1, M + 1, 1):\n",
    "    S[t] = S[t - 1] * (np.exp((r - rj - 0.5 * sigma ** 2) * dt\n",
    "                       + sigma * np.sqrt(dt) * sn1[t])\n",
    "                       + (np.exp(mu + delta * sn2[t]) - 1)\n",
    "                       * poi[t])\n",
    "    S[t] = np.maximum(S[t], 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "uuid": "19508067-6759-4e88-9276-0d21a0be9e8e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fVDe/GBGfaTXV0fO02sOYmZld5a/FrsyvD6t3KUvu9bU/hnsb1mVNexh1B4wtwNkRcZek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\negAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8f11908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(S[-1], bins=50)\n",
    "plt.xlabel('value')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: jd_hist\n",
    "# title: Simulated jump diffusion at maturity\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false,
    "uuid": "27046a97-3c3c-4265-bde7-45f9b71dc001"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9ugZ0pWvdrnSu07lCHcH/5kjSET75+xOeCXqGPg363LR2iyM5P5+OBw+SZjSyq00bGpYw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\nEMmK4yuYfXA2Jy6cwN3BnadbPM3zbZ6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cpMDlclBaupyCgtkUFMzGZhPzYUDAEKKj/4eo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\nsajpVAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x76e3ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(S[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: jd_paths\n",
    "# title: Simulated jump diffusion paths\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance Reduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false,
    "uuid": "293a9f5c-7ae1-4994-b11d-64ba5312559a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Mean  Std. Deviation\n",
      "-------------------------------\n",
      "-0.011870394558  1.008752430725\n",
      "-0.002815667298  1.002729536352\n",
      "-0.003847776704  1.000594044165\n",
      "-0.003058113374  1.001086345326\n",
      "-0.001685126538  1.001630849589\n",
      "-0.001175212007  1.001347684642\n",
      "-0.000803969036  1.000159081432\n",
      "-0.000601970954  0.999506522127\n",
      "-0.000147787693  0.999571756099\n",
      "-0.000313035581  0.999646153704\n",
      "-0.000178447061  0.999677277878\n",
      " 0.000096501709  0.999684346792\n",
      "-0.000135677013  0.999823841902\n",
      "-0.000015726986  0.999906493379\n",
      "-0.000039368519  1.000063091949\n"
     ]
    }
   ],
   "source": [
    "print \"%15s %15s\" % ('Mean', 'Std. Deviation')\n",
    "print 31 * \"-\"\n",
    "for i in range(1, 31, 2):\n",
    "    npr.seed(1000)\n",
    "    sn = npr.standard_normal(i ** 2 * 10000)\n",
    "    print \"%15.12f %15.12f\" % (sn.mean(), sn.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false,
    "uuid": "5940d5f7-72ed-4fd2-8a48-d66c2d5e45db"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8410000"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i ** 2 * 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false,
    "uuid": "732f2ba4-3133-4508-92a1-10ee47519f36"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000L,)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn = npr.standard_normal(10000 / 2)\n",
    "sn = np.concatenate((sn, -sn))\n",
    "np.shape(sn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false,
    "uuid": "3f166fbb-ed57-403f-b251-1b5579ec261d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Mean  Std. Deviation\n",
      "-------------------------------\n",
      " 0.000000000000  1.009653753942\n",
      "-0.000000000000  1.000413716783\n",
      " 0.000000000000  1.002925061201\n",
      "-0.000000000000  1.000755212673\n",
      " 0.000000000000  1.001636910076\n",
      "-0.000000000000  1.000726758438\n",
      "-0.000000000000  1.001621265149\n",
      " 0.000000000000  1.001203722778\n",
      "-0.000000000000  1.000556669784\n",
      " 0.000000000000  1.000113464185\n",
      "-0.000000000000  0.999435175324\n",
      " 0.000000000000  0.999356961431\n",
      "-0.000000000000  0.999641436845\n",
      "-0.000000000000  0.999642768905\n",
      "-0.000000000000  0.999638303451\n"
     ]
    }
   ],
   "source": [
    "print \"%15s %15s\" % ('Mean', 'Std. Deviation')\n",
    "print 31 * \"-\"\n",
    "for i in range(1, 31, 2):\n",
    "    npr.seed(1000)\n",
    "    sn = npr.standard_normal(i ** 2 * 10000 / 2)\n",
    "    sn = np.concatenate((sn, -sn))\n",
    "    print \"%15.12f %15.12f\" % (sn.mean(), sn.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false,
    "uuid": "de17794f-4dfd-4441-8d0f-bd097ac0da2c"
   },
   "outputs": [],
   "source": [
    "sn = npr.standard_normal(10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false,
    "uuid": "0251bf81-b4d8-4828-80be-9ff972204d06"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.001165998295162494"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "uuid": "a59c5234-0398-4260-9bcb-d63cd6a7c917"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99125592020460496"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false,
    "uuid": "699ea494-9c78-4ddc-b153-ce291039f77e"
   },
   "outputs": [],
   "source": [
    "sn_new = (sn - sn.mean()) / sn.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false,
    "uuid": "e5836915-236c-4c1b-9012-20fb52e50608"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.3803181647963357e-17"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn_new.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "uuid": "5113ce74-07a2-4b16-b8d0-7ed9495ccb9b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999999999999989"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn_new.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "uuid": "f566cd19-61d3-4c69-9391-cb1c906d23c3"
   },
   "outputs": [],
   "source": [
    "def gen_sn(M, I, anti_paths=True, mo_match=True):\n",
    "    ''' Function to generate random numbers for simulation.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    M : int\n",
    "        number of time intervals for discretization\n",
    "    I : int\n",
    "        number of paths to be simulated\n",
    "    anti_paths: boolean\n",
    "        use of antithetic variates\n",
    "    mo_math : boolean\n",
    "        use of moment matching\n",
    "    '''\n",
    "    if anti_paths is True:\n",
    "        sn = npr.standard_normal((M + 1, I / 2))\n",
    "        sn = np.concatenate((sn, -sn), axis=1)\n",
    "    else:\n",
    "        sn = npr.standard_normal((M + 1, I))\n",
    "    if mo_match is True:\n",
    "        sn = (sn - sn.mean()) / sn.std()\n",
    "    return sn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Valuation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### European Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false,
    "uuid": "693f44be-b3dd-4820-9610-a127f0e9b31b"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "sigma = 0.25\n",
    "T = 1.0\n",
    "I = 50000\n",
    "def gbm_mcs_stat(K):\n",
    "    ''' Valuation of European call option in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation (of index level at maturity)\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K : float\n",
    "        (positive) strike price of the option\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0 : float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    sn = gen_sn(1, I)\n",
    "    # simulate index level at maturity\n",
    "    ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "                 + sigma * np.sqrt(T) * sn[1])\n",
    "    # calculate payoff at maturity\n",
    "    hT = np.maximum(ST - K, 0)\n",
    "    # calculate MCS estimator\n",
    "    C0 = np.exp(-r * T) * 1 / I * np.sum(hT)\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false,
    "uuid": "f325da52-3e45-4e9e-a4a2-067efb1c3bb7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.071786484995128"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_stat(K=105.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false,
    "uuid": "511974d5-5ceb-4b68-bf7f-e01eaa43f7c6"
   },
   "outputs": [],
   "source": [
    "M = 50\n",
    "def gbm_mcs_dyna(K, option='call'):\n",
    "    ''' Valuation of European options in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation (of index level paths)\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K : float\n",
    "        (positive) strike price of the option\n",
    "    option : string\n",
    "        type of the option to be valued ('call', 'put')\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0 : float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    dt = T / M\n",
    "    # simulation of index level paths\n",
    "    S = np.zeros((M + 1, I))\n",
    "    S[0] = S0\n",
    "    sn = gen_sn(M, I)\n",
    "    for t in range(1, M + 1):\n",
    "        S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "                + sigma * np.sqrt(dt) * sn[t])\n",
    "    # case-based calculation of payoff\n",
    "    if option == 'call':\n",
    "        hT = np.maximum(S[-1] - K, 0)\n",
    "    else:\n",
    "        hT = np.maximum(K - S[-1], 0)\n",
    "    # calculation of MCS estimator\n",
    "    C0 = np.exp(-r * T) * 1 / I * np.sum(hT)\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false,
    "uuid": "44ae2961-ec7c-4e69-b6ff-17b8093a894b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.950876029854153"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_dyna(K=110., option='call')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "uuid": "bedb79ae-4f01-41ea-b16a-22ea9781fc0e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.618957750716017"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_dyna(K=110., option='put')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false,
    "uuid": "e9e52ba0-6ccb-46df-a089-49505d6c7919"
   },
   "outputs": [
    {
     "ename": "ImportError",
     "evalue": "No module named bsm_functions",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-81-7f6f9b8d29cc>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[0mbsm_functions\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mbsm_call_value\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mstat_res\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mdyna_res\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0manal_res\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mk_list\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m80.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m120.1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m5.\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mImportError\u001b[0m: No module named bsm_functions"
     ]
    }
   ],
   "source": [
    "from bsm_functions import bsm_call_value\n",
    "stat_res = []\n",
    "dyna_res = []\n",
    "anal_res = []\n",
    "k_list = np.arange(80., 120.1, 5.)\n",
    "np.random.seed(200000)\n",
    "for K in k_list:\n",
    "    stat_res.append(gbm_mcs_stat(K))\n",
    "    dyna_res.append(gbm_mcs_dyna(K))\n",
    "    anal_res.append(bsm_call_value(S0, K, T, r, sigma))\n",
    "stat_res = np.array(stat_res)\n",
    "dyna_res = np.array(dyna_res)\n",
    "anal_res = np.array(anal_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false,
    "uuid": "3f9f44ec-47de-4891-bf82-2b620c647c9a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hqKPgqquCq+83bIg5OBEBoins3wQ+D7wJvEEwQc03IminZGVpLCfNlOdoHDVu\nHBdXVABsfOTsRRUV/PDuc/j2t4Opbk8+GbbfHo4/PpjydsmSYK572XI6juORpTyHPgeVuy8HTgz7\ne0UkHequfr/02mt5fdkyHtthB0YUPLhm9OhgvzffhMceg0cfDcbrO3cOJs754hfh8MODwi8i4UvV\n89hbS2PsIunmDosWBUX+0UeDW+sGDYIjjggK/fDhwVX4ItIyid3HHhcVdpHS8umn8I9/BEX+scfg\nn/+E/fbbdEa/336a016kKXFfPCfNyNJYTpopz9FrbY632iqY+OaHPwzO3pctgwsuCK66P+ss6NMH\njj02uK9+0aL2PT6v4zgeWcpz6P8mNrMuwHFAecH3u7v/OOy2RCQbtt0Wjj46WACWL4fHHw/O6H/2\nM1i3btPZ/BFHBPPci0hxUdzH/jDwHvBPYH3ddne/upnP3QqMAt52933y23oBvwN2BmqBE9z9vSKf\nVVe8SEa5B1fV143PP/54MFFOXaE/7LDg6XUi7Uncz2Nf6O57t+JzwwlmrLuzoLBfBbzj7leZ2QVA\nT3e/sMhnVdhF2on162HevE2F/u9/h3333VTohw0LpsgVybK4x9ifNLMtnmXO3WcTPAmu0DHAHfnX\ndwDHtjG2VMjSWE6aKc/RSyLHZWXBxXUXXhgU9v/8B3784+BBNuefH4zPjxwJv/gFPPvspolyZtXU\ncEl1NZOqqrikurpk5rbXcRyPLOU5iutOhwNnmNkrwJr8Nm/llLJ98/fFAywH+oYRoIhkx9Zbbzpb\nB3j3XZg5Myj6118P778P++9Rw6BF47n2P5vmuL84P9+9nkonWRNFYT86gu/E3d3MGu1vHzt2LOXl\n5QD06NGDyspKqqqqgE3/EkvLet22tMSjda23dr2qqipV8QA8+2yO3r3h+uuD9XvvzXH7hEkbi3qw\nd/DgmnMuu5Y1nbZhq63SE79+L7RebL3udW1tLc2J7D52M/sM0KVu3d1fa8FnyoEHC8bYFwNV7r7M\nzPoBM9199yKf0xi7iDRqUlUVk57Y/ME1o7oeRo4cQ4fCQQcFt+AddBD0Vd+gpFzcz2M/xsxeBF4B\nniC4mn1aK79uKnB6/vXpwJ/bHGAKFP4LTKKjPEevVHK8rnPxB9cMHd6FpUth4sTglrsbboDdd4eK\nCjjlFPjVr4IL9datizngAqWS41KXpTxH0RV/GXAQ8Ii7DzGzLwCnNvchM7sHOAzoY2avAz8ErgB+\nb2Znkr8dqMeEAAAgAElEQVTdLYJ4RSTjjho3jouXLKn3HPmLKioYcc45dO9ef4x+wwZYvBjmzIEn\nnwwmyXnjjeCCvboz+mHDoHfvhP4yIs2I4na3f7r758xsATDU3dfreewikrRZNTU8cu21lK1ezfou\nXTiy4ME1zXn3XXjqqaDQz5kDc+cGk+TUFfqDD4Y99oAOmstTYhL3feyPAv8NXA70Ad4G9nP3g0Nt\nqH6bKuwiEpv162Hhwk2F/skn4Z13gjP5ukJ/4IGaOEeiE/d97McCHwPnAtOBl4AvR9BOycrSWE6a\nKc/Ra685LiuDwYPhW9+CO++El16CF14I1j/5BH7yk+CMft99g7nvb789eL815x/tNcdxy1Keo3ge\n+6r81e27uvvtZtYVKAu7HRGRNPnMZ4Jn0dc9j37tWliwIDijnz49uEDvo4+CM/q6s/r992/8cbWz\namqYMWUKbyxfzqN9+3LUuHG6515aJIqu+G8AXwd6uXuFmf0XcL27HxFqQ/XbVFe8iKTem29u6rqf\nMyeYGW/33evfaldeDrMfquHh8ePrXex3cUUF1ZMnq7gLEP8Y+wLgAODv7j4kv+25unvTo6DCLiKl\naPVqeOaZ+mP1AEM3VFPz9ozN9r+0upqfTJ8ec5SSRnGPsa9x97qpZDGzjoCqboEsjeWkmfIcPeW4\nbbp0Cc7Uv/c9+OMf4a23ggI/sNfGn9CNM+UBvPXiah5/HFasiD3UzMvSsRzFfexPmNnFQFczOxI4\nG3gwgnZERDLFLOiK7z2wMyze/P331nVh4sSgC3+77YIL+CorNy277KJb7iSarvgy4EzgqPymh4Gb\no+wrV1e8iGTJrJrNx9gvqqhgRH6MfcMGqK2F+fPrL++9t3mx32uvoGdAsiXWMfZ8g52B3Qm64Be7\n+9rQG6nfngq7iGRKaybUWbEiuBK/sNi/+CLsuuvmBb9Pn5j+IhKJuC+eGwX8Gng5v2kQcJa7PxRq\nQ/XbLKnCXvikJomO8hw95Th6bc3x6tXw/PObF/xu3eoX+spKGDSo/Xbll9qx3FRhj2KM/RfAF9z9\npXzjFcBD+UVERGLUpQsMHRosddzrd+X/5jdw/vmwcmUwqU5doR88GPbeO3jmvZSOKM7Y/+Hu+xes\nGzC3cFvYSu2MXUQkjd59d9OZfd2f//53cCbf8Ox+++03/3zdpDod16xhXefOmlQnQnF3xf8aGAj8\nPr/peOA14BEAd78/1AZRYRcRicqaNbBo0eYX6m2zTf0z+3Ura1j4s/H8rybViUXchf32/Mu6L7aC\n17j7GaE2SOkV9lIbyylVynP0lOPopTHH7vDqq/UL/YqHq5m9evNJdc4fXs2Vj0+nYxQDvyFKY56b\nEusYu7uPDfs7RUQkPeruty8vh2OPDbZNqloDT2y+77/mrmbbbaGiAnbbLZhCd7fdNi09e8YZefsQ\nxRn7AGAKcEh+0yxgvLu/EWpD9dssqTN2EZGsuaS6mstmFJ8Gd8L903nxxWC8fvHi4M+6pWvX+gW/\n7s/yclJ/lp+kJJ7H/lvgrvymk4GT3f3INnxnLfABsB741N0PaPC+CruISIKam1SnGPdgGt2GBX/x\nYli2bNNZfsMzfZ3lJ/AQGHcf3Ny2LfzOV4DPufu7jbxfUoW91MZySpXyHD3lOHqllOPWTKrTmI8/\nZuNZfsPC3/Asv+51W87ySynPEP997CvM7FTgboIL5/4f8E4I31v0LyAiIulw6KhRoV0B37VrcLX9\n4AanhMXO8h95pPVn+Vl87n0UZ+w7A9cBw/KbngTOcffX2vCdLwPvE3TF3+DuNzV4v6TO2EVEJHyf\nfBKc5Tfs1m/sLH/V0hqevbI0b9GLrSs+/4jWO9z95NC+NPjefu6+1My2J7gf/hx3n13wvgq7iIgU\nVXiWX1jsP36imllFbtErhefex9YV7+7rzGxnM+tc+Ez2EL53af7P/5jZn4ADgNmF+4wdO5by8nIA\nevToQWVl5cbxkrrn7KZl/Zprrkl1fFlZr9uWlniyuN4w10nHk8V1/V6Et96/P3TokGOPPYL1SVVr\nyBXcolcF5IDXly3buC0t8de9rq2tpTlRdMX/huDJblOBj/Ob3d1/0crv6wqUufuHZrYNMAP4kbvP\nKNinpM7YcyV2kUapUp6jpxxHTzmOTuEtejmCwg6lf8YeRWGflH9Zb+Y5d/9RK79vF+BP+dWOwG/d\n/fIG+5RUYRcRkeS15ha9tIj9eexxU2EXEZHWCPMWvTjFfcY+s8hmd/fDQ22ofpslVdjVtRYP5Tl6\nynH0lON4lFqe476P/fsFr7sAxwHrImhHREREGoilK77hM9oj+P6SOmMXERFpi1jP2M2sV8FqB2A/\noHvY7YiIiMjmOkTwnc8A/8wvc4DzgTMjaKdkFd6XKNFRnqOnHEdPOY5HlvIcxfPYy8P+ThEREWmZ\n0MbYzewH7n5V/vXx7v6Hgvf+190vCqWh4m1rjF1ERNqNpsbYw+yKH1PwumERPzrEdkRERKQRUYyx\nSzOyNJaTZspz9JTj6CnH8chSnlXYRUREMiTMMfb1bHroy9bAJwVvb+3uUUyGU9e2xthFRKTdiOU+\ndncvC+u7REREpHXUFZ+ALI3lpJnyHD3lOHrKcTyylGcVdhERkQzRY1tFRERKTFz3sYuIiEjCSqKw\nm9kIM1tsZi+a2QVJx9NWWRrLSTPlOXrKcfSU43hkKc+pL+xmVgZcB4wA9gTGmNkeyUbVNvPnz086\nhHZBeY6echw95TgeWcpz6gs7cADwkrvXuvunwL3A6IRjapP33nsv6RDaBeU5espx9JTjeGQpz6VQ\n2PsDrxesv5HfJiIiIg2UQmHP3OXutbW1SYfQLijP0VOOo6ccxyNLeU797W5mNgyY5O4j8usTgA3u\nfmXBPun+S4iIiISssdvdSqGwdwT+DRwBvAXMBca4+6JEAxMREUmhyB7MEhZ3X2dm3wEeBsqAW1TU\nRUREikv9GbuIiIi0XClcPCciIiItpMIuIiKSISrsIiIiGaLCLiIikiEq7CIiIhmiwi4iIpIhKuwi\nIiIZosIuIiKSISrsIiIiGaLCLiIikiEq7CIiIhmiwi4iIpIhKuwiIiIZosIuIiKSISrsIiIiGaLC\nLiIikiEq7CIiIhmiwi4iIpIhKuwiIiIZosIuIiKSISrsIiIiGaLCLiIikiGJFnYzG2Fmi83sRTO7\noJF9qsxsnpktNLNczCGKiIiUFHP3ZBo2KwP+DXwReBP4BzDG3RcV7NMD+BtQ7e5vmFkfd38nkYBF\nRERKQJJn7AcAL7l7rbt/CtwLjG6wz0nAH939DQAVdRERkaYlWdj7A68XrL+R31bos0AvM5tpZk+b\n2amxRSciIlKCOibYdkvGALYChgJHAF2BOWb2d3d/MdLIRERESlSShf1NYEDB+gCCs/ZCrwPvuPsn\nwCdmNgsYDNQr7GaWzIUCIiIiCXF3K7Y9ya74p4HPmlm5mXUCTgSmNtjnAeAQMyszs67AgcDzxb7M\n3UtmmThxYuIxtIdFeVaOs7Aox8pzsaUpiZ2xu/s6M/sO8DBQBtzi7ovM7Kz8+ze4+2Izmw48C2wA\nbnL3ooVdREREku2Kx92nAdMabLuhwfrPgZ/HGVfUamtrkw6hXVCeo6ccR085jkeW8qyZ5xJQWVmZ\ndAjtgvIcPeU4espxPLKU58QmqAmTmXkW/h4iIiItYWZ4IxfPJdoVLyISJbOiv3ub0YmBZIm64hOQ\ny+WSDqFdUJ6jVxo59maWdCuNHJe+LOVZhV1ERCRDNMYuIpkVdMU399tg6oqXktPUGLvO2EVERDJE\nhT0BWRrLSTPlOXrKcfSU43hkKc8q7CIiIhmiMXYRySyNsUsxWbgNUvexi4iI1NP8P/hKlbriE5Cl\nsZw0U56jpxxHTzmOSy7pAEKjwi4iIpIhGmMXkczSGLsUk4XjQvexi4iItBMq7AnQmFk8lOfoKcfR\nU47jkks6gNCosIuIiGSIxthFJLOyMJYq4cvCcaExdhERkXZChT0BGjOLh/IcPeU4espxXHJJBxAa\nFXYREZEMSXSM3cxGANcAZcDN7n5lI/vtD8wBTnD3+4u8rzF2EdlMFsZSJXxZOC5SOcZuZmXAdcAI\nYE9gjJnt0ch+VwLTKeXJe0VERGKQZFf8AcBL7l7r7p8C9wKji+x3DnAf8J84g4uSxszioTxHTzmO\nnnIcl1zSAYQmycLeH3i9YP2N/LaNzKw/QbG/Pr8pvf0iIiIiKZBkYW9Jkb4GuDA/gG5kpCu+qqoq\n6RDaBeU5espx9JTjuFQlHUBoknwe+5vAgIL1AQRn7YU+B9wbXOhAH+BoM/vU3ac2/LKxY8dSXl4O\nQI8ePaisrNz4P0RdV5bWta719re+qYu1sfXgM2mJV+vxrG9St17VYJ3UxZvL5aitraU5iV0Vb2Yd\ngX8DRwBvAXOBMe6+qJH9bwMezMJV8YU/IhId5Tl6ac9xFq5+TnuOS1Hx4yJH/bP2dB8XTV0Vn9gZ\nu7uvM7PvAA8T3O52i7svMrOz8u/fkFRsIiIipUpzxYtIZmXhjF3Cl4XjIpX3sYuIiEj4VNgTsPnF\nGxIF5Tl6ynH0lOO45JIOIDQq7CIiIhmiMXbJhPwtkc3ScdK+ZGEsVcKXheMilVfFi4Sv+f9RRUSy\nrsVd8Wb2ZTPLmdlTZvbtKIPKOo2ZxSWXdACZp2M5espxXHJJBxCaRgu7mQ1psOk04HDgIOBbUQYl\nIiIirdPoGLuZ3UjQd3mpuy8zs18A7wEbgOHuXh1fmE3TGLtkYcxMwqfjQorJwnHR1Bh7kxfPmdlg\n4MfAP4FfAMOArsDD7r4mglhbRYVdsvA/qoRPx4UUk4XjotUT1Lj7AncfDcwHHgB2dPepaSrqpUhj\nZnHJJR1A5ulYjp5yHJdc0gGEpqkx9m+Z2ZNmNofgLH0E0NPMZpjZobFFKCIiIi3W1Bj7c8C+QCdg\njrsPzW/vSTDu/t3YomyGuuIlC11rEj4dF1JMFo6LVo2xm9l0YBawDVDu7idHF2LbqLBLFv5HlfDp\nuJBisnBctHaMfTSwEJhNcKubhERjZnHJJR1A5ulYjp5yHJdc0gGEptGZ5/IXyE2NMRYRERFpI80V\nL5mQha41CZ+OCykmC8eFnscuIiLSTrSosJtZmZntaGYD65aoA8syjZnFJZd0AJmnYzl6ynFcckkH\nEJpmn+5mZucAE4G3gfUFb+0TVVAiIiLSOs2OsZvZEuAAd18RT0hbTmPskoUxMwmfjgspJgvHRVvH\n2F8DPgg3JBEREYlCSwr7K8BMM5tgZufnl9TMOleKNGYWl1zSAWSejuXoKcdxySUdQGhaesb+KMHU\nstsC3fJLm5nZCDNbbGYvmtkFRd4/2cwWmNmzZvY3M9s3jHZFRESyKrH72M2sDPg38EXgTeAfwBh3\nX1Swz0HA8+7+vpmNACa5+7Ai36Ux9nYuC2NmEj4dF1JMFo6LpsbYG70q3swmu/t4M3uwyNvu7se0\nMa4DgJfcvTbf3r0E09huLOzuPqdg/6eAndrYpoiISKY11RV/Z/7PqxtZ2qo/8HrB+hv5bY05E3go\nhHYTpzGzuOSSDiDzdCxHTzmOSy7pAELT1Fzx/8z/mYuo7Rb3cZjZF4CvAp9vbJ+xY8dSXl4OQI8e\nPaisrKSqqgrY9D9GWtbnz5+fqniysr5J0+tpiVfr8axv+u/f2HrwmbTEq9+LeNY3aXo9TfHmcjlq\na2tpTpJj7MMIxsxH5NcnABvc/coG++0L3A+McPeXGvkujbG3c1kYM5Pw6biQYrJwXKR1rvingc+a\nWbmZdQJOpMHT5PJT194PnNJYURcREZFNWlzYzaxrmA27+zrgO8DDwPPA79x9kZmdZWZn5Xf7IdAT\nuN7M5pnZ3DBjSMrmXUESjVzSAWSejuXoKcdxySUdQGhaMlf8wcDNBPeuDzCzSuAb7n52Wxt392nA\ntAbbbih4/TXga21tR0REpL1oyVzxc4GvAA+4+5D8tn+5+14xxNciGmOXLIyZSfh0XEgxWTgu2jzG\n7u6vNdi0rs1RiYiISOhaNKWsmX0ewMw6mdn3KJhERracxszikks6gMzTsRw95TguuaQDCE1LCvu3\ngG8TTB7zJjAkvy4iIiIpk9h97GHSGLtkYcxMwqfjQorJwnHRpjF2M7vTzHoUrPc0s1vDDFBERETC\n0ZKu+H3d/b26FXdfCQyNLqTs05hZXHJJB5B5OpajpxzHJZd0AKFpSWE3M+tVsNILKIsuJBEREWmt\nltzHfhpwMfB7wIDjgZ+6+51NfjBGGmOXLIyZSfh0XEgxWTgumhpjb9HFc2a2F3A4QSYed/fnww2x\nbVTYJQv/o0r4dFxIMVk4LsJ4CMxigoexPAisyj+cRVpJY2ZxySUdQObpWI6echyXXNIBhKYlc8Wf\nA0wE3gbWF7y1T1RBiYiISOu0ZIx9CXCAu6+IJ6Qtp654yULXmoRPx4UUk4Xjoq1d8a8BH4QbkoiI\niEShJYX9FWCmmU0ws/Pzy3ejDizLNGYWl1zSAWSejuXoKcdxySUdQGiaHWMnOGN/DeiUX0RERCSl\nWjxXvJlt4+4fRRxPq2iMXbIwZibh03EhxWThuGjrXPEHm9nzBLe8YWaDzexXIccoIiIiIWjJGPs1\nwAjgHQB3XwAcFmVQWVcKY2Zm1qIl3XJJB5B5pXAslzrlOC65pAMITUvG2HH31xr8iK+LJhxJl+a7\nqkREJF1ach/7fcD/AdcBBwLjgP3c/f9FH17LaIw9fKU2BlVq8Uo8dFxIMVk4Ltp6H/s3gW8D/YE3\ngSH59TACG2Fmi83sRTO7oJF9puTfX2BmQ8JoV0REJKuaLOxm1hGY7O4nuftn3H17dz85jFnozKyM\noBdgBLAnMMbM9miwz0hgV3f/LPAN4Pq2tpsGGjOLSy7pADJPx3L0lOO45JIOIDRNFnZ3XwfsbGad\nI2j7AOAld69190+Be4HRDfY5BrgjH8tTQA8z6xtBLCIiIpnQkovnXgH+amZTgY/z29zdf9HGtvsD\nrxesv0Ewht/cPjsBy9vYdqKqqqqSDqGdqEo6gMzTsRw95TguVUkHEJqWFPYl+aUDsG2Ibbf0qoSG\nFwek92oGERGRhDVb2N19EkQy89ybwICC9QEEZ+RN7bNTfttmxo4dS3l5OQA9evSgsrJy479068ao\nklpv6f3edVdgJh3vpjG9lsWteFu3nsvl+NGPftRkrBMnTtz4uaTjraqqatGxPHPmzNTEG2g+5lwu\nl5p4S+33otTiLdXfi7rXtbW1zcbcktvdDgZuBrq5+wAzGwyc5e5nN/vtTX9vR+DfwBHAW8BcYIy7\nLyrYZyTwHXcfaWbDgGvcfViR70r17W6b31qRY/Nun3TfWlGKCn+sJRzNH8s6jtuq1H4vsnDrGJTe\n70VTt7u1pLDPBb4CPODuQ/Lb/uXue4UQ2NEEM9uVAbe4++VmdhaAu9+Q36fuyvmPgDPc/Zki31Ni\nhb3oXqk/8EWaP5Z1HLdVqf1elFq8WdHmwu7uB5jZvILCvsDdB0cQa6uosIvEQ4U9eqX2e1Fq8WZF\nWyeoec3MPp//ok5m9j1gUTOfkSblkg6gXSgcm5Ko5JIOoB3IJR1Au5Cl34uWFPZvEdHMcyIiIhKu\nRrvizexKd7/AzE5w99/HHNcWUVe8SDzUFR+9Uvu9KLV4s6K1XfGjLPgvNiGasERERCRsTRX2acBK\nYB8z+7DB8kFM8WVULukA2oUsjZmlVy7pANqBXNIBtAtZ+r1oqrBf6u49gBp379Zg6R5XgCIiItJy\nTY2xP+PuQ83sLnc/Jea4tojG2EXioTH26JXa70WpxZsVTY2xNzWlbGczOxk42Mz+h/rz77m73x9m\nkCIiItJ2TXXFfxMYDmwHfBn4UsHy5ehDy7Jc0gG0C1kaM0uvXNIBtAO5pANoF7L0e9HoGbu7zwZm\nm9k/3P2WGGPKqJY9cEBERKQtmhpjP8LdHzOz4ygygJKmrvi0j7GLZIXG2KNXamPWpRZvVrR2jP1Q\n4DGCbvdi/0VSU9hFREQk0OgYu7tPzP851t3PaLjEF2L2ZGksJ82U5zjkkg6gHcglHUC7kKXfi0bP\n2M3s/PzLov0n7v6LSCISERGRVmtqjH0SQVHfDdgfmEpwBdiXgLlpurddY+wi8dAYe/RKbcy61OLN\nirY+j302MNLdP8yvdwMecvfhoUfaSirsIvFQYY9eqRXKUos3K9r6PPbPAJ8WrH+a3yatlKWxnDRT\nnuOQSzqAdiCXdADtQpZ+L5q6Kr7OncBcM7ufoCv+WOCOSKMSERGRVmm2Kx7AzD5HMAudA7PcfV7U\ngW0JdcWLxENd8dErta7tUos3K9o0xl4KVNhF4qHCHr1SK5SlFm9WtHWMXUKWpbGcNFOe45BLOoB2\nIJd0AO1Cln4vVNhFREQyJLGueDPrBfwO2BmoBU5w9/ca7DOA4OK9zxD09dzo7lOKfJe64kVioK74\n6JVa13apxZsVae2KvxB4xN3/i2BO+guL7PMpcJ677wUMA75tZnvEGKOIiEhJSbKwH8Om2+buILiN\nrh53X+bu8/OvVwGLgB1jizAiWRrLSTPlOQ65pANoB3JJB9AuZOn3IsnC3tfdl+dfLwf6NrWzmZUD\nQ4Cnog1LRESkdLVkgppWM7NHgB2KvHVx4Yq7u5k1OgBjZtsC9wHj82fumxk7dizl5eUA9OjRg8rK\nSqqqqoBN/xJLy3rdtrTEo3Wtb8n6pjPIqvxSuJ58fKW+HshRl8/N13MUSl+8dfGlM95SXa97XVtb\nS3OSvHhuMVDl7svMrB8w0913L7LfVsBfgGnufk0j36WL50RioIvnoldqF6OVWrxZkdaL56YCp+df\nnw78ueEOFhwxtwDPN1bUS1Hhv8AkOspzHHJJB9AO5JIOoF3I0u9FkoX9CuBIM3sBODy/jpntaGY1\n+X0+D5wCfMHM5uWXEcmEKyIikn6aUlZEWkxd8dErta7tUos3K9LaFS8iIiIhU2FPQJbGctJMeY5D\nLukA2oFc0gG0C1n6vVBhFxERyRCNsYtIi2mMPXpBjpuXljxrjD0ZTY2xRzpBjYiIbBkVQGkrdcUn\nIEtjOWmmPMchl3QAmafjOB5ZyrMKu4iISIZojF1EWkxj7NKQxtiTofvYRURE2gkV9gRkaSwnzZTn\nOOSSDiDzdBzHI0t5VmEXERHJEI2xi0iLaYxdGtIYezI0xi4iItJOqLAnIEtjOWmmPMchl3QAmafj\nOB5ZyrMKu4iISIZojF1EWkxj7NKQxtiToTF2ERGRdkKFPQFZGstJM+U5DrmkA8g8HcfxyFKe9XQ3\nERFpo5Y9albioTF2EWkxjbGLpIPG2EVERNqJRAq7mfUys0fM7AUzm2FmPZrYt8zM5pnZg3HGGKUs\njeWkmfIch1zSAWSejuN4ZCnPSZ2xXwg84u7/BTyWX2/MeOB5mr+fomTMnz8/6RDaBeU5KlawfKHB\nuoRNx3E8spTnpAr7McAd+dd3AMcW28nMdgJGAjeToV+N9957L+kQ2gXlOXzuXm+ZOHHiZtskXDqO\n45GlPCdV2Pu6+/L86+VA30b2+z/g+8CGWKISEREpcZHd7mZmjwA7FHnr4sIVd3cz2+yf+Wb2JeBt\nd59nZlXRRJmM2trapENoF5Tn6CnH0VOO45GlPCdyu5uZLQaq3H2ZmfUDZrr77g32+V/gVGAd0AXo\nDvzR3U8r8n3q/xMRkXalsdvdkirsVwEr3P1KM7sQ6OHujV5AZ2aHAd9z9y/HFqSIiEgJSmqM/Qrg\nSDN7ATg8v46Z7WhmNY18RmflIiIizcjEzHMiIiIS0MxzMTCzCWb2LzN7zszuNrPOWzJJjzTPzMbn\n87vQzMbntynHbWBmt5rZcjN7rmBboznNH+cvmtliMzsqmahLTyN5Pj7/m7HezIY22F953kKN5Phn\nZrbIzBaY2f1mtl3BeyWdYxX2iJlZOfB1YKi77wOUAf+PLZukR5pgZnsDXwP2BwYDXzKzCpTjtroN\nGNFgW9GcmtmewInAnvnP/MrM9PvSMsXy/Bzw38Cswo3Kc6sVy/EMYC93Hwy8AEyAbOS4pIItUR8A\nnwJdzawj0BV4ixZO0iMtsjvwlLuvdvf1wBPAcSjHbeLus4GVDTY3ltPRwD3u/qm71wIvAQfEEWep\nK5Znd1/s7i8U2V15boVGcvyIu9fNkfIUsFP+dcnnWIU9Yu7+LnA18BpBQX/P3R+h5ZP0SPMWAsPz\n3cRdCWYr3AnlOAqN5XRH4I2C/d4A+scZWDuhPEfjq8BD+dcln2MV9ojlu4TPBcoJDphtzeyUwn3y\nz5zVVYyt5O6LgSsJutamAfOB9Q32UY5D1oKcKt/xUJ7bwMwuBta6+91N7FZSOVZhj95+wJPuvsLd\n1wH3AwcBy8xsB4D8JD1vJxhjyXP3W919P3c/jKDL7QVguXIcusZy+iYwoGC/nfLbJFzKc4jMbCxB\nD9/JBZtLPscq7NFbDAwzs63NzIAvEjyt7kHg9Pw+pwN/Tii+TDCzz+T/HAj8D3A3MBXlOGyN5XQq\n8P/MrJOZ7QJ8FpibQHxZVDi7mPIcEjMbQfAsktHuvrrgrZLPse5jj4GZ/YDgR3AD8AzBFdzdgN8D\nA4Fa4AR3z87jhWJmZrOA3gQXKp7n7jPNrBfKcauZ2T3AYUAfgvH0HwIP0EhOzewigrHKdcB4d384\ngbBLTpE8TwTeBa7Nb3sfmOfuR+f3V563UCM5ngB0Isg1wBx3Pzu/f0nnWIVdREQkQ9QVLyIikiEq\n7CIiIhmiwi4iIpIhKuwiIiIZosIuIiKSISrsIiIiGaLCLiKNMrNzzWzrJt6/ycx2z79eFV9kItIY\n3ccuIo0ys1eA/dx9RZH3OhQ8HQsz+9Ddu8UaoIhsRmfsIgKAmW1jZjVmNt/MnjOzHxI8uGimmT2W\n32eVmf3czOYDB5lZzsyGNviePmb2pJkdbWbbm9l9ZjY3vxycwF9NpF3pmHQAIpIaI4A33X0UgJl1\nB6yElXUAAAE3SURBVM4AqvKPHwboCvzd3b+X36del19+zv6pwMXu/piZ3Q38n7v/LT+P/3Rgz3j+\nOiLtkwq7iNR5Fvi5mV0B/MXd/xo8t6ie9cAfG/l8J+Ax4Gx3n53f9kVgj4Lv6WZmXd3943BDF5E6\nKuwiAoC7v2hmQ4BRwGVm9niR3VZ74xfmfAo8TXDmX1fYDTjQ3deGHrCIFKUxdhEBNj5ffbW7/xb4\nOTAE+ADo3sKvcIInYu2ef6IhwAxgXEEbleFFLCLF6IxdROrsA/zMzDYAa4FvAQcD083sTXc/gqB4\nN8bd3c1sDDDVzD4gKOq/NLMFBL83TwBnR/q3EGnndLubiIhIhqgrXkREJENU2EVERDJEhV1ERCRD\nVNhFREQyRIVdREQkQ1TYRUREMkSFXUREJENU2EVERDLk/wORXzjhg8LzhQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9766210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(8, 6))\n",
    "ax1.plot(k_list, anal_res, 'b', label='analytical')\n",
    "ax1.plot(k_list, stat_res, 'ro', label='static')\n",
    "ax1.set_ylabel('European call option value')\n",
    "ax1.grid(True)\n",
    "ax1.legend(loc=0)\n",
    "ax1.set_ylim(ymin=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (anal_res - stat_res) / anal_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('difference in %')\n",
    "ax2.set_xlim(left=75, right=125)\n",
    "ax2.grid(True)\n",
    "# tag: opt_val_comp_1\n",
    "# title: Comparsion of static and dynamic Monte Carlo estimator values\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false,
    "uuid": "3f9f44ec-47de-4891-bf82-2b620c647c9a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ld9lF/fIiSRbbWPFmVgV0Baa4++ch1qPELtIKn39ev19+883rnrA/8MCN++U1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\niMEuSdKEGOySJE2IwS5J0oQY7JIkTchPVsq13d6tTu8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9766b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(8, 6))\n",
    "ax1.plot(k_list, anal_res, 'b', label='analytical')\n",
    "ax1.plot(k_list, dyna_res, 'ro', label='dynamic')\n",
    "ax1.set_ylabel('European call option value')\n",
    "ax1.grid(True)\n",
    "ax1.legend(loc=0)\n",
    "ax1.set_ylim(ymin=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (anal_res - dyna_res) / anal_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('difference in %')\n",
    "ax2.set_xlim(left=75, right=125)\n",
    "ax2.grid(True)\n",
    "# tag: opt_val_comp_2\n",
    "# title: Comparsion of static and dynamic Monte Carlo estimator values\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### American Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false,
    "uuid": "033296d5-230b-4b35-ae3f-a2a7ed8c8937"
   },
   "outputs": [],
   "source": [
    "def gbm_mcs_amer(K, option='call'):\n",
    "    ''' Valuation of American option in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation by LSM algorithm\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K : float\n",
    "        (positive) strike price of the option\n",
    "    option : string\n",
    "        type of the option to be valued ('call', 'put')\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0 : float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    dt = T / M\n",
    "    df = np.exp(-r * dt)\n",
    "    # simulation of index levels\n",
    "    S = np.zeros((M + 1, I))\n",
    "    S[0] = S0\n",
    "    sn = gen_sn(M, I)\n",
    "    for t in range(1, M + 1):\n",
    "        S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "                + sigma * np.sqrt(dt) * sn[t])\n",
    "    # case based calculation of payoff\n",
    "    if option == 'call':\n",
    "        h = np.maximum(S - K, 0)\n",
    "    else:\n",
    "        h = np.maximum(K - S, 0)\n",
    "    # LSM algorithm\n",
    "    V = np.copy(h)\n",
    "    for t in range(M - 1, 0, -1):\n",
    "        reg = np.polyfit(S[t], V[t + 1] * df, 7)\n",
    "        C = np.polyval(reg, S[t])\n",
    "        V[t] = np.where(C > h[t], V[t + 1] * df, h[t])\n",
    "    # MCS estimator\n",
    "    C0 = df * 1 / I * np.sum(V[1])\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false,
    "uuid": "18dba6e2-2a7f-4474-bbee-227f354fcbc3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.7451001544286395"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_amer(110., option='call')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false,
    "uuid": "a82c68fc-9820-43a7-8302-3ae0f5a47650"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.706157996453983"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_amer(110., option='put')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false,
    "uuid": "2c4a0f35-5a41-416b-aa39-53d78d1cc366"
   },
   "outputs": [],
   "source": [
    "euro_res = []\n",
    "amer_res = []\n",
    "k_list = np.arange(80., 120.1, 5.)\n",
    "for K in k_list:\n",
    "    euro_res.append(gbm_mcs_dyna(K, 'put'))\n",
    "    amer_res.append(gbm_mcs_amer(K, 'put'))\n",
    "euro_res = np.array(euro_res)\n",
    "amer_res = np.array(amer_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false,
    "uuid": "6304932d-114f-43b1-ae59-4b0ad2de33fc"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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11UkGDCiyeDfb1u8L/b6oja2qqgqgrt5l0pQm8R2BicChqV2zgXHu/n4O7y1n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\noMAHN0e8OOGGtJkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e967b550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(8, 6))\n",
    "ax1.plot(k_list, euro_res, 'b', label='European put')\n",
    "ax1.plot(k_list, amer_res, 'ro', label='American put')\n",
    "ax1.set_ylabel('call option value')\n",
    "ax1.grid(True)\n",
    "ax1.legend(loc=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (amer_res - euro_res) / euro_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('early exercise premium in %')\n",
    "ax2.set_xlim(left=75, right=125)\n",
    "ax2.grid(True)\n",
    "# tag: opt_euro_amer\n",
    "# title: Comparsion of European and LSM Monte Carlo estimator values\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Risk Measures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Value-at-Risk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "uuid": "5473289e-2301-40fb-a665-2d33d43ea09a"
   },
   "outputs": [],
   "source": [
    "S0 = 100\n",
    "r = 0.05\n",
    "sigma = 0.25\n",
    "T = 30 / 365.\n",
    "I = 10000\n",
    "ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "             + sigma * np.sqrt(T) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "uuid": "b2eed114-77e7-479b-b20b-d36a0ffbe636"
   },
   "outputs": [],
   "source": [
    "R_gbm = np.sort(ST - S0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "uuid": "b53e5254-96cc-4294-8ef7-76a2cf21cbca"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SnjzzSyRJj6P9g5d9FM2t6qp6ger73wF30/4lyAeBn+547k20i5kHgBdWHesi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\nZtbl/wO8NYzvUc7TIAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e138e650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(R_gbm, bins=50)\n",
    "plt.xlabel('absolute return')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: var_hist_gbm\n",
    "# title: Absolute returns of geometric Brownian motion (30d)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false,
    "uuid": "768aa308-d5c2-4f5d-9936-c19c9321996a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Level    Value-at-Risk\n",
      "---------------------------------\n",
      "           99.99           26.072\n",
      "           99.90           20.175\n",
      "           99.00           15.753\n",
      "           97.50           13.265\n",
      "           95.00           11.298\n",
      "           90.00            8.942\n"
     ]
    }
   ],
   "source": [
    "percs = [0.01, 0.1, 1., 2.5, 5.0, 10.0]\n",
    "var = scs.scoreatpercentile(R_gbm, percs)\n",
    "print \"%16s %16s\" % ('Confidence Level', 'Value-at-Risk')\n",
    "print 33 * \"-\"\n",
    "for pair in zip(percs, var):\n",
    "    print \"%16.2f %16.3f\" % (100 - pair[0], -pair[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false,
    "uuid": "b9952498-c4ad-4d5a-8d3c-3bce1d71006d"
   },
   "outputs": [],
   "source": [
    "dt = 30. / 365 / M\n",
    "rj = lamb * (np.exp(mu + 0.5 * delta ** 2) - 1)\n",
    "S = np.zeros((M + 1, I))\n",
    "S[0] = S0\n",
    "sn1 = npr.standard_normal((M + 1, I))\n",
    "sn2 = npr.standard_normal((M + 1, I))\n",
    "poi = npr.poisson(lamb * dt, (M + 1, I))\n",
    "for t in range(1, M + 1, 1):\n",
    "    S[t] = S[t - 1] * (np.exp((r - rj - 0.5 * sigma ** 2) * dt\n",
    "                       + sigma * np.sqrt(dt) * sn1[t])\n",
    "                       + (np.exp(mu + delta * sn2[t]) - 1)\n",
    "                       * poi[t])\n",
    "    S[t] = np.maximum(S[t], 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false,
    "uuid": "37cfd26e-2c44-456a-8b8b-56cf10e12aac"
   },
   "outputs": [],
   "source": [
    "R_jd = np.sort(S[-1] - S0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false,
    "uuid": "3300cad0-872b-45ef-9b12-3fc3507b2c54"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZLoo5m4HFTfOjxb85FB8G32SsEP4gsITiL8k6FcK/DlyQpi8CvjbZe6nTA/jv\nwA1p+gzgsZzyt7yXdoXwWuenuOrzw8DPtbTXPj/FH6zfpCiEzyGPQrgoaqIfa2lfB6xI0yupeSE8\n5bwAuHsq+SsPP4U3+xsUY6H/BhwE7m167jqKot8u0reSUvtiYEd67hNVv4emXK9IHdoI8BXgnMne\nS50eFN96+Uzat1uBoZzyt7yXfx7tNHLJD+wBHgW2pcenMsv/OopvIO0FVlWdp0TeX6GoBYw07fPL\ngLnA/cBu4D5goOqsJd7LBYx9e6qj/D65z8zMSptJ354yM7Mec6dhZmaludMwM7PS3GmYmVlp7jTM\nzKw0dxpmZlaaOw2bFSQ9PQ3rGJb0yUmW+U+Srup2W+Os+4R0Fr5ZZdxp2GwxHScklVnHfODNU92A\nknGePhFYPoV1+v+5TRv/MtmMIulvJP1juknOO1ue+2hqvz9dIwtJ16ab6myXdFtqmyvpztT2FUln\nj66iaV3rJf1m0/xTaXIt8Op0k5v3SDom3SxpS1rff2uTeVDSP0m6heLs+tMlvb/pNR9qWveL07rX\nSbpg9EY6aT1/JGlZmt4naa2krcAb0/yHJG2V9JCkl3a1o23WcqdhM83bI+IVwLnAtZJOTO3Po7i2\n1y8BXwRWp/YVFDfWeRnFtbQAbgC2prbrKK431Gq8o44VwAMRcU5E3Ai8A3giIs6juIfEO9NltVu9\nBPjfKd+ZwEvSa84BFkt6dVr3N9O6P8DRV+WNplwBPB4RiyPic2n+exGxGPhj4PfGyW82IXcaNtO8\nR9LotbxOp7jnBxTXDPpcmv4LiusIATwEbJD0FuCnqe1VFNfUIiI2Ay+UdHzJ7bd+kF8K/FdJ24Cv\nUlzn5yVtXvdojN0o7FLg0vSarcBL02smunR7O59rmb8j/ft1igsFmnWslpdGN5uKdI+Ai4DzI+Lf\nJW2muAT0UYsy9hf5rwG/Cvw6cH27oaik9cjiJ6Q/ulLNYM4E0a6JiE2TxP9hy/wfRMSf/kzoo49Q\njmRInjPJOn+U/v0p/r9vU+QjDZtJXgD8IHUYZwLnNz13DPDGNP1m4IFUcP6FiGhQXBL6BIp7Pz8A\nvAWOdETfi+L2ns32UVw9GYrbZR6Xpp8Cmo9KPg8sl3RsWt8Zkp47yfv4PPB2Sc9LrzlV0s+3Wfej\nwEJJcyQNABdOsl6zrvmvDZtJNgLvkrST4pLbX2l67ofAeZI+SHFLyzdR/P5/RtIJFEcWN0bEv6bC\n882StqfAIQpaAAAAlElEQVTXLUvraK4Z/Bnwt2kobCMw2qlsB36a2j8NfIJiKOjrqZP6LsXl/Vsd\nOZKJiE2SzgK+kr5I9TTwloj4lqT/K2kHcE9ErJB0O/ANivuBfH2CfRMt0768tU2JL41uZmaleXjK\nzMxKc6dhZmaludMwM7PS3GmYmVlp7jTMzKw0dxpmZlaaOw0zMyvNnYaZmZX2/wHDncAJrgGvmgAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e0eee250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(R_jd, bins=50)\n",
    "plt.xlabel('absolute return')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: var_hist_jd\n",
    "# title: Absolute returns of jump diffusion (30d)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false,
    "uuid": "8adcca19-77bf-4d8e-a342-1a5cc1cadd69"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Level    Value-at-Risk\n",
      "---------------------------------\n",
      "           99.99           75.029\n",
      "           99.90           71.833\n",
      "           99.00           55.901\n",
      "           97.50           45.697\n",
      "           95.00           25.993\n",
      "           90.00            8.773\n"
     ]
    }
   ],
   "source": [
    "percs = [0.01, 0.1, 1., 2.5, 5.0, 10.0]\n",
    "var = scs.scoreatpercentile(R_jd, percs)\n",
    "print \"%16s %16s\" % ('Confidence Level', 'Value-at-Risk')\n",
    "print 33 * \"-\"\n",
    "for pair in zip(percs, var):\n",
    "    print \"%16.2f %16.3f\" % (100 - pair[0], -pair[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false,
    "uuid": "812884b3-c147-4799-8b7a-93eb62a9b1fc"
   },
   "outputs": [],
   "source": [
    "percs = list(np.arange(0.0, 10.1, 0.1))\n",
    "gbm_var = scs.scoreatpercentile(R_gbm, percs)\n",
    "jd_var = scs.scoreatpercentile(R_jd, percs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false,
    "uuid": "b960f3cc-fed3-4cfa-9189-040931e4ab09"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-90.0, 0.0)"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PArd567cD9wN1NXxbXRK4NoXbbnN3DC1awAUXuMdWN2yAwsKgozPGpKHdJggR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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9c21890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(percs, gbm_var, 'b', lw=1.5, label='GBM')\n",
    "plt.plot(percs, jd_var, 'r', lw=1.5, label='JD')\n",
    "plt.legend(loc=4)\n",
    "plt.xlabel('100 - confidence level [%]')\n",
    "plt.ylabel('value-at-risk')\n",
    "plt.grid(True)\n",
    "plt.ylim(ymax=0.0)\n",
    "# tag: var_comp\n",
    "# title: Value-at-risk for geometric Brownian motion and jump diffusion\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Credit Value Adjustments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false,
    "uuid": "92795f2e-84b4-4881-960f-91a39eb1cc77"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "sigma = 0.2\n",
    "T = 1.\n",
    "I = 100000\n",
    "ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "             + sigma * np.sqrt(T) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false,
    "uuid": "3e3c6a61-c268-44f4-bce9-f3c2f83faac9"
   },
   "outputs": [],
   "source": [
    "L = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false,
    "uuid": "f06f2c7d-8c1a-4cc3-b171-dad76994c6b9"
   },
   "outputs": [],
   "source": [
    "p = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false,
    "uuid": "38b71c82-76a1-4299-992f-93820cbf2677"
   },
   "outputs": [],
   "source": [
    "D = npr.poisson(p * T, I)\n",
    "D = np.where(D > 1, 1, D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false,
    "uuid": "46418aea-2253-4f09-840a-1c45676bda2c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100.16378042785578"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(-r * T) * 1 / I * np.sum(ST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false,
    "uuid": "fe7436d3-4eb4-40f4-9d4c-c5efa0e3d3a0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.50372915651713923"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CVaR = np.exp(-r * T) * 1 / I * np.sum(L * D * ST)\n",
    "CVaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false,
    "uuid": "3070c8f6-8a77-4373-b423-f6871170dbaf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.660051271338617"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0_CVA = np.exp(-r * T) * 1 / I * np.sum((1 - L * D) * ST)\n",
    "S0_CVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false,
    "uuid": "d7d14139-b76d-4c11-a57b-930db11abd3c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.496270843482861"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0_adj = S0 - CVaR\n",
    "S0_adj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false,
    "uuid": "c6995617-5021-4d8f-9f94-8fca0571ff89"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1013"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(L * D * ST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false,
    "uuid": "fc6e6717-9ffc-486c-a736-3892c277f3e6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 175)"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9DWu2YVzT+25JFwMHSHo/2UF2t870Dc26aeLUk9moKVIwVpEd1f0w8DvAbcB/GWRQoy71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\nuGCYmVkh/x+qGvchuO7TQQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x777c080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(L * D * ST, bins=50)\n",
    "plt.xlabel('loss')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "plt.ylim(ymax=175)\n",
    "# tag: cva_hist_stock\n",
    "# title: Losses due to risk-neutrally expected default (stock)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false,
    "uuid": "59b7c831-c915-4c06-a23b-0ac913220d76"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.427336109660052"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K = 100.\n",
    "hT = np.maximum(ST - K, 0)\n",
    "C0 = np.exp(-r * T) * 1 / I * np.sum(hT)\n",
    "C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "uuid": "da0198e3-10bc-4324-8e0e-b09c2e61e94d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.053822578452208093"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CVaR = np.exp(-r * T) * 1 / I * np.sum(L * D * hT)\n",
    "CVaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false,
    "uuid": "24d26328-f3f2-4da4-8d5c-7fb06a70eec8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.373513531207843"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C0_CVA = np.exp(-r * T) * 1 / I * np.sum((1 - L * D) * hT)\n",
    "C0_CVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "uuid": "a221dbb8-eec3-45e1-abd7-146050c0285f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "582"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(L * D * hT)  # number of losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false,
    "uuid": "e1becbb6-7a1e-49bb-8a8e-b7daab189c6e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1031"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(D)  # number of defaults"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false,
    "uuid": "44c3d031-8002-4bba-abd7-0db5451b2d52"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43995"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I - np.count_nonzero(hT)  # zero payoff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false,
    "uuid": "b132d24e-093b-45e6-a4cc-29b8ef006038"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 350)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e114a490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(L * D * hT, bins=50)\n",
    "plt.xlabel('loss')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "plt.ylim(ymax=350)\n",
    "# tag: cva_hist_opt\n",
    "# title: Losses due to risk-neutrally expected default (call option)\n",
    "# size: 60"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
